Electronic – How is a Twisted Pair’s +-2.5v used to send a 1 or a 0

One pair is used to transmit, the other - to receive.

If you connect two computers without a switch or a hub, in the past you had to use a cross-over cable, where one pair is connected to pins 1,2 on one end and pins 3,6 on the other end. Hubs had reversed pinout of the socket, so you can use a straight cable to connect a PC to a hub, but would need a cross-over cable to connect two hubs (unless one hub had an "uplink" port).

Modern Ethernet devices can be connected with any cable - they will figure out whether the cable is straight or crossed and will reconfigure themselves accordingly. Gigabit Ethernet works a bit differently - it uses all pairs (instead of just two) and can reconfigure each pair as "transmit" or "receive" as needed.

Now, as to why pairs are used instead of single wires:

To transfer data, you need to be able to get some current to the receiving device. As we know current only flows when there is a closed circuit, so you need at least two wires connecting the devices. Your "scheme 2" will not work as you drew the "batteries" not connected. This can be done in one of two ways - easier is to have one or more data wires and one ground wire (called Single Ended system). Here ground is shared among all the signals and you need less wires. However, this system does not work well for long distances - noise can get in the cable quite easily and the receiving device may not be able to understand the transmission. One solution is to use a coaxial cable (it shields the data wire from noise), but they are expensive and you would need one cable for each data pin. Still, multiple coax cables are used, say, for connecting a VGA monitor to the computer (at least in the better monitor cables). It is also true for analog audio.

A better way to do things is to have two wires for each signal. Now you send the signal in both wires, but invert one of them, that is, if you send "1" in one wire, you send "0" on the other - so the voltage between those two wires is always non-zero. You also use a twisted pair cable. This is called differential signaling. Now, the noise affects both wires in a pair equally and the receiver can cancel it out (by measuring the voltage between the wires instead of each wire to ground). This allows the signal to be sent further using cheaper twisted pair cables. Professional analog audio also uses differential signalling for, say, microphones etc (the XLR connectors have three pins - positive signal, negative signal and ground), so that longer cables can be used without noise affecting the signal.

An example of differential signalling:

As you see, in this case what matters is the polarity of the received voltage, so if whatever noise affects both wires the same, the polarity will not change and the information will still be transmitted.

To transmit in both directions (but not at the same time, so-called "half-duplex") over the same pair of wires you can do it like this:

Now when any switch is closed, both lamps light up, so any end can transmit taking turns. This arrangement is called "open collector".

As Andy says in the comment, for low speed signals over short distances you can use almost any cable for any purpose. Where your step pulses are likely at most 10kHz signals they are many orders of magnitude slower than what we would consider the tipping point where it could become problematic.

Even 100kHz or 1MHz for the distance between a control board and a motor board will not see any problems.

If you run the "low frequency" step signal through a wire of a pair and put the direction signal through the other wire, as long as the direction signal is actively driven to Vcc and GND it should not notice too much of it. Again, it's a small distance and at low frequency over small distances twisted pair is just another bunch of wires that are close to each other.

EDIT: Little more added while modifying the schematic below

If you want to use "low frequency" and get a little reflection immunity with only a single component, you could add a resistor at the transmitter side of the pulse signal, so that the reflections get "tied down" at the transmission side.

But this requires the output resistance of your driver to be known as compared to the signal on the other wire to work properly.

To avoid a lot of look-up or testing you can try 75 Ohm if the other wire is a hard ground or 50 Ohm if it is also driven by a modern digital chip's output. Many logic chips have internally something between 15 and 40 Ohm output impedance, but that's very general and may well be wrong in specific situations.

I averaged it into about 25 Ohm, in which case if you use ground on the other wire and as such just one output and then add a 75 Ohm resistor that adds up to 100 Ohm on the TX side. If you use two outputs (direction signal on the other wire) that will be two pins of 25 Ohm, so you only need 50 Ohm to add up to 100 Ohm.

To note: This is not a very neat trick and it involves a lot of guess work (since the PCB also has certain impedances and the whole trick with the resistors will then mismatch those, etc, etc), so you should avoid it if you can and use proper Differential drivers and receivers when single ended start to be so quick that you start seeing problems.

End of Addition

Some sideways thinking about higher speeds (Also Edited):

If you ever do need higher speed with single ended pulses, you can quite easily modify the system to at least reduce the problems over the cable. It's far from perfect, but it will be a little better than nothing, if for some mysterious reason a true differential driver isn't possible:

^{simulate this circuit – Schematic created using CircuitLab}