Problems:
First, currents don't "come from" the positive terminal. That's a very common misconception, an error called the "sequential fallacy" appearing widely in grade-school electricity textbooks. The basic problem is that wires are not like empty pipes. And, power supplies don't fill them up. Instead, wires are already pre-filled with charge, so that currents always appear everywhere in a circuit, all at the same time. ("Current" means charge-flow. When a circle of movable charges starts flowing, "current" appears in the entire ring. That's the basic circuit rule.)
In other words, electric circuits behave like flywheels and drive-belts. In the same way, the metal of a bike-chain doesn't "come from" a particular location on the sprocket. It doesn't "start out" at one point. Instead, the entire circle is made of chain, just like the entire circuit is made of movable electrons. Also, all the chain was there before any power supply existed. With bike chains, when a force is applied, the whole thing turns. With circuits, when a potential difference is applied, all the movable charges inside the ring (inside the circuit,) they all start moving as a unit, like a solid chain going in a complete circle. But those charges were already inside the wires before any battery was connected. Wires are like water-filled hoses.
Second, electric potential can only exist between two points, and one single spot on a circuit never "has a voltage." This is true because voltage is a bit like altitude: an object cannot "have an altitude," since height can only be measured between two points. It's meaningless to discuss the height or elevation or altitude of an object. Altitude above what? Above the floor? Above the ground outside the building? Altitude above Earth's center? Any object will have infinitely many altitudes at the same time!
Voltage has exactly the same problem: one terminal can only "have a voltage" when compared to another terminal. Voltage acts like distance: voltage and distance are double-ended measurements. Or in other words, one terminal in a circuit always has many different voltages at the same time, depending on where we place the other meter lead.
Third, in circuits the driving force is provided by the positive and the negative power supply terminals, both at the same time. And, most important: the path for current is through the power supply. Power supplies are short circuits. An ideal power supply acts like a zero-ohm resistor. Think about it: in a dynamo coil, the charges pass through the coil and back out again. The wire has a very low resistance. Same thing with batteries: the path for current is through the battery and back out again. The battery plates are shorted out by very conductive electrolyte.
Example:
- Here's a correct description of a flashlight. The charges "start out"
inside the tungsten filament. When the switch is closed and the
circuit is complete, one end of the filament gets charged positive,
the other negative. This forces the filament's own charges to start
flowing. The charges move out of the filament and into one wire,
while at the same time, more charges are coming into the other end of
the filament. These charges are supplied by the metal wires (and,
before the switch was turned on, all the conductors were already full
of movable charges.) Continuing, the charges that were in the
filament will flow out into one wire, move slowly to the battery
(takes minutes or hours to get there,) then flow through the battery
and back out again. They exit from the battery's other terminal,
flow back to the other end of the filament, finally ending up where
they started. A "complete circuit." The charges are like an endless
drive-belt, or like a rotating flywheel or a bike-chain. The battery
pushes the charges, but it doesn't supply the charges. The copper
and the tungsten supply the charges which flow in the flashlight
circuit. The density of charges throughout the circuit is constant (like a water-filled pipe with no bubbles.) Charges move quite slowly, but since they all start moving
at the same time, the light bulb lights up instantly, even if the
wires are quite long.
Fourth: any positive ions inside a battery are extremely movable. They're certainly not locked in place. If they were, then batteries would be insulators, and wouldn't work. Some batteries are based on the flow of positive ions in one direction and negative ions in the other. Lead-acid batteries are different. In the acid, only the protons are flowing. Acids are proton-conductors.
But beware: batteries give added complexity which can derail an explanation.
Instead, replace your flashlight battery with a big coil, and a supermagnet. Connect it to the light bulb. Shove the supermagnet into the coil, and the light bulb flashes briefly. Where did the charges come from? How can a moving magnet create charges? IT DOESN'T. Dynamos and batteries are charge-pumps. The moving magnet forces the wire's own charges to start moving. (A pump does not supply the stuff being pumped!) The moving magnet causes a current, because it applies an EM pumping-force to the movable charges already inside the metal.
Bad conductor. Bad!
Here's a clarification. Many intro textbooks provide the wrong definition of "conductor;" totally wrong, and extremely misleading. They'll teach you that conductors "let charges pass through" (or, that 'electricity' passes through, or 'current.') Nope. Conductors aren't like hollow pipes. Conductors aren't transparent to electricity. Instead, the word "conductor" actually means "a material which is full of mobile charges." Conductors are like tanks full of water. They're like aquariums, or like pre-filled pipes. Conductors obey ohm's law: whenever we apply a voltage-difference to the ends of a wire, the flow of the conductor's own charges depends on the wire resistance: I = V/R. It is the wire's mobile charge which does the flowing. Think about it, vacuum is an insulator. How can vacuum block the flow of charges? Vacuum does not need to, as there are no movable charges present in a vacuum. That is what makes it an insulator.
All of this leads to an important concept. Whenever we take a piece of wire and hook the ends together to form a closed loop, we've created an "invisible drive-belt," a loop of movable charge inside the non-moving wire. Thrust a magnet-pole into the metal loop, and all the charges of the wire will move as one, rotating like a flywheel. It's a ring-shaped swimming pool, and if we push on the water, we can get all the water turning like a flywheel, while the swimming pool itself remains still.
FIFTH, currents aren't backwards, because electric currents aren't flows of electrons.
Specifically, the polarity of the flowing charges depends on the type of conductor. Yes, in solid metals, the movable charges are electrons. But there are large numbers of conductors where no electrons can move. The closest ones are your brain and nervous system: simultaneous flows of positive and negative atoms in opposite directions: moving ions, with no electron-flows at all. The "Electrolytes," salt water including the damp ground and the oceans; these are not electron-conductors.
Weirder example: acids are conductive because they're full of +H positive hydrogen ions. Another name for an +H ion is... "the proton." When we put some amperes through acid, the current is a flow of protons. (Heh, if there's any ground-currents in the dirt, and also the dirt is acidic rather than salty, then those underground currents are proton-flows! )
In other words, "amperes" can be electrons flowing, or protons flowing, or positive sodium passing through negative chloride going the other way. Or, fast electrons going one way in a spark, while slow nitrogen ions go forward or back depending on whether they're pos- or neg-ionized. And in p-type semiconductors, the current is a flow of valance-band electrons, the "lattice vacancies" in the crystal! (Each vacancy exposes an excess silicon proton, so the vacancies each carry a genuine positive charge. "Holes" move by electron-transfer, yet each hole really is positively charged.)
With all the above complexity, how can we possibly describe what's happening inside circuits? Easy: it's already done for us. We conceal the moving charges and ignore them. We ignore their flow-speed, and their quantity. We ignore their polarity. Instead we add up all the various charges which might be inside any conductor, calculate the total flow-rate, and call this "amperes." Is your conductor a hose full of salt water? Put a clamp-on ammeter around it, and read off the amperes. The ion density doesn't matter. The ion speed doesn't matter, and it could even be an acid-hose full of protons, instead of a seawater-hose.
Amps is amps.
Amperes are also called "conventional current," or just "electric current."
Very important: amperes are not charge-flow. A conductor might have one amp, but this doesn't tell us anything about the charges inside. There could be a few charges flowing fast, or lots of charges flowing slow. There could be positive charges going forwards, or neg going backwards, or both at the same time (as with human bodies receiving DC electric shock.) All that stuff is covered up, and all we have left is the amperes ...amperes of conventional current.
OK, back to GND versus COM versus EARTH.
"Ground" is confusing because the word is nearly always used incorrectly.
In circuits, we almost always choose one power supply terminal to be the "common," and we connect one voltmeter-lead to it. It's not grounded, so we really shouldn't call it "ground" (it's not connected to a metal stake driven into dirt!) Instead the "common" is just the traditional point for making voltage readings. We never explicitly explain this fact (it's a silent agreement!) Since voltages are complicated double-ended measurements, things are simplified if we pretend that they're single-ended. So, hook your black voltmeter lead to the "circuit common," then ignore it.
Now pretend that the red-colored probe on your voltmeter can actually measure the voltage OF A TERMINAL. But terminals can't "have a voltage!" Yes, exactly right. But we silently pretend that they do. Any point on the circuit can have a voltage ...in relation to another circuit point. If we were talking about altitudes, we could always make our measurements in relation to sea-level. Next, never mention sea-level, then finally pretend that objects and locations can "have an altitude," when actually that's impossible, since altitude is a length; a distance and not a location.
So, all the new students typically get confused when we discuss the "voltage of a terminal." Actually we meant "the voltage that appears between a terminal and the Circuit Common." But that's too much to repeat all the time. We're silently saying "voltage between, voltage between," while we actually say "voltage at this spot," or at that other spot over there. Then all the new students start thinking that one single terminal can have a voltage, even though voltage doesn't work like that.
Is our negative supply terminal the Circuit Common? Yes, usually. I've seen very old radios with PNP transistors, and a negative main supply with "positive ground." The positive battery terminal is the Circuit Common. All the measurements in that schematic were negative voltages. Besides 1950s transistor radios, the same thing happens in old VW Beetles, and in some motorbikes. The positive battery terminal is connected to the chassis, so the "supply terminal" is the negative one. Don't install a normal car-radio in an old VW, because it will short out or catch fire when you turn on the ignition. Power supply was backwards.
All we gotta do is get rid of all collectible 1950s Japanese PNP-transistor radios, VW beetles, and positive-grounded motorcycles, and then Circuit Common will always and forever be the negative supply terminal! Well, unless it's some weird, electrically-floating industrial sensor system with a mix of AC power and virtual-ground op-amp circuits.
Best Answer
There are two ways to answer this question: an engineering one, and a physical one. While many engineers prefer to think in an engineering way only (sometimes they can't even explain how the stuff really works), I believe that knowing the concepts is very important. Therefore, I'll try to answer your question from a physical point of view (which is much longer). You may scroll straight to the end of the page to find an engineering answer.
The electricity is all about electric charges and their movement. Really, nothing more. The only interesting question in electricity is: "Given the initial configuration of charges, what will be their configuration in some future time (or what was it in some past time)?". You might ask yourself now: "But what about electric and magnetic fields? What about resistance, capacitance and inductance? What about semiconductors? Isn't all these concepts are basis to the electricity theory?". The answer is: no, they aren't. We'll get to definitions of fields later, but all other terms merely describe in which way a particular object affects the charges which are moving through it or initially present inside it.
I'll try to describe the layers underlying the abstraction that we call "Electrical Engineering". I'll try to show the exact steps which lead from elementary particles to operational amplifiers, transformers and etc.
Electric charge and force:
Physicist found that the electrical properties of any particle (particle = elementary particle) may be accurately described by a single quantity - an electric charge. The charge may be positive or negative, and its magnitude may vary for various particles. An electrical interaction between two particles is completely determined by particles' charges and their polarity (positive or negative). The interaction is either attractive or repulsive (attractive for particles having opposite polarities, repulsive for particles having the same polarities). The complete description of interaction between two particles may be given with a single mathematical construct - a force vector.
NOTE: in further sections I'll use terms "particle" and "charge" interchangeably while referring to a single particle.
Electric Field:
You can't describe a single particle using a force concept because force is defined as an interaction between two particles; the field, on contrary, is particle's specific. Single particle's electric field is a mathematical description (mathematically: vector field) of the effect (electric force) that this particle has on any other particle in the universe, divided by the other particle's charge. In other words: force = field*(charge of the other particle). Note that the field does not exist by itself, it is just a convenient way to describe a presence of a particle: instead of saying "there an electric charge over there" one says "the field here is", and this change in terminology is very convenient because it allows for "localization" of the problem to some bounded region.
Magnetic Field:
Magnetic field is a field (mathematically: vector field) which describe the effect (magnetic force) of a moving particle on any other moving particle in the universe. Magnetic force and magnetic field are related in a bit complicated fashion, therefore I won't describe it here. You'll find a lot of material on the Internet. In fact, this is one of the concepts which may be studied only if you need it. One important fact to remember: magnetic field is always created by moving charges and acts only on moving charges. One unimportant, but interesting fact to remember: magnetic field is in fact an electric field which is transformed by special relativity's effects.
(Electrostatic) Energy:
Energy is one of the broadest concepts in physics. Essentially, you may think of energy either as an abstraction of a single type of particles' interactions, or a "bridge" that brings various types of interactions to a common denominator (or both).
Electrostatic energy abstracts electrostatic interactions. It is defined as an amount of work you can get from a combination of charges. You may notice that I replaced the term "energy" by another one - "work". It is because I find it very difficult to explain either one. Many graduated physicist do not entirely understand these concepts. In a few words: you must perform work in order to move a charge in an electric field, and the work done on the charge you moved causes the charge's energy to increase by amount of work done. The good news are that you don't need to understand the physical meaning of energy and work in order to become a good engineer. When the term "energy" is used by the engineers, it refers to the actual energy you can use in order to do "work". For example: dissipate the energy stored in a battery on some conductor in order to produce heat, or heat with light, etc...
However, there is very important fact about the electrostatic energy which you must remember: no matter what path a charge made while moving from A to B, the increase (or, maybe, decrease) in its energy will always be the same (the work done is the same). It may sound obvious to some people: "well, of course it is this way!", but it is not! Think about moving a table from point A to B in the room - it is obvious that if you take the table out of the room and then bring it back, it will take you more energy (in this case chemical energy of your body) than if you moved it from A to B in a straight line. While the above counter example is not scientifically correct, it emphasizes the point: if a charge moves from A to B the amount of work done is independent of the path!
(Electrostatic) Potential:
Potential is a term which exists in both Electrical Engineering and in physics, which is not uncommon. But it is uncommon that this term's definition and usage is the same in this two disciplines. In a sense, one can say that this term is a boundary between physics and electrical engineering.
The main purpose of potential is to describe how the energy of a particle changes when it moves in a space. Since I couldn't explain the physical concept of "energy", I can't describe the physical concept of potential. However, from engineering point of view the concept is relatively simple: there are various potentials at various points in my system. If a particle moves from point A to point B, it gains (or loses) an energy of \$(P_B-P_A)*Q\$, where \$P_x\$ is the potential at point \$x\$ and \$Q\$ is the charge of a particle.
The most important and the most confusing fact about potentials to remember: the magnitude of the potential at a single point is meaningless, only the difference between points is significant (because it represents the energy a charge may gain if it moves between these points).
One can't overestimate the importance of the above statement. It becomes the Alfa-and-Omega of electrical engineering once combined with additional basic axiom from physics world: each particle will always try to minimize its energy. It is the reason for current flow once you provide a path: if the charges can lower their energy while moving to another potential, they'll do so.
Let's take another angle of view on the most important statement on potentials (What was it? You don't remember?!?! Go back and read again the statement in bold!!!): I didn't really explain how one can calculate the potential. Bad news: it is impossible without additional information. Good news: the additional information would be just a single number which you can choose! What the hell am i talking about? Well, first of all, I got bored a bit, therefore I'm starting to write in a very annoying way. However, the above statement is totally true - the potential is defined up to a constant, which you're free to choose, but it must be the same constant for all the potentials in your system. Look at this equation: \$E_{gained} = (P_{final} - P_{initial})*Q\$. Add whatever constant you want to both \$P\$'s (the same constant), the result for energy gained will be the same! This is the reason we can define a reference potential in our circuit as we wish - the only thing that matters is potential difference, and this will remain constant if we shift all the potentials in the system by some constant.
Voltage:
Voltage between points is just a shorthand for "difference in potentials between points". Note the word "difference" - the voltage is never defined for a single point in a circuit. It is always a difference. The usual practice is to define some node in a circuit as 0 of potential, and then calculate voltages of other points relative to this zero. Why can we do this? Well, go back and read the section on potentials. Still don't get it? Well, go back to the previous statement starting with "well" and execute it.
Many electrical circuit are actually connected to either Earth (the planet, yes) or something which is very "big" (can take in significant amount of charge without changing its potential). There are many reasons to do this, but none of them directly related to your question. When such a connection exists, it is usually the most convenient potential to be taken as zero. This reference is called "ground". However, as you know now, it is just a matter of convenience. You could say that ground is at potential 100 and calculate all other potentials in the system relative to it. In circuits which are not connected to Earth or similar, ground zero is usually taken as the most negative potential - this approach ensures that you'll need to work with non-negative potentials only. While convenient, it is not a major thing.
Closing the loop:
If anybody really read until here - I'm really impressed and it is a great honor to me. I'm sure that all the above information can't settle down in a (normal) human's head after being read once. What is important, is that you will remember the two sentences in bold, and know how to get from the first to the second. It is my belief that you'll be a bit more of an engineer if you know to do this.
Every abstract term in engineering can be explained in terms of electrical charges and their movement: the potential, the voltage, the resistance, the capacitance, the inductance, the semiconductors etc... However, engineers must do real work, and if you want to be productive you must work at the highest level of abstraction available for your task.
Engineering Answer:
The actual potentials are not important - only the differences (voltages) are. You can put your led into a circuit with negative potentials and it will work (as long as it has suitable voltage across it, and the polarity of voltage is correct).
The question about the circuit with resistors is tricky. The tricky part is the voltage source - these bastards are sometimes internally connected to ground. Let's assume that your voltage source is floating, i.e not connected to ground (a battery, for example). In this case, in order to understand what will happen in your circuit, you can shift all the potentials by +6. This will make the minus port of voltage source a zero potential, the plus port will become +12, and the ground will be +6. If the notion of +6 volts on ground pin disturbs you - erase the "GND" label. Look at your circuit - now you can easily analyze it. It is obvious that the current through both resistors will be the same because the voltages across them are the same.
If you want to keep the "GND" label and still feel comfortable with the shift of +6 volts in potentials - consider reading the whole answer again (or for the first time :))
Wow, this was the hell a lot longer than I intended!