Overload and short-circuit protection protect against two different parameters being exceeded: heat (power integrated over a relatively short time) and current.
A high current can be a an almost instantaneous problem: a wire that can't shed its heat can get too hot and burn through, or set fire to surrounding materials. In a real short-circuit situation the voltage is ~ zero, so the power delivered by the supply is ~ zero.
Overload is a slightly longer-term situation, where the heat in the motor is the problem. A motor has much more heat capacity than a wire, so a peak is not an immediate problem, but over a slightly longer period the heat must still be limited.
Your question contains one very common misconception, and that is that large amounts of current flowing through ground is normal.
In this diagram, notice the lack of a particular path for current flow into or out of ground. As long as everything remains balanced and a power line isn't touching the earth or a tree, there is no path for current to travel through ground (except some minor leakages).
Here is a wye connected four wire system. Notice how the ground is connected directly to the neutral point in the center, and the neutral (N) line has no coil. In this system, the neutral line is the return path for all single phase loads - that is, anything that is connected from a phase to the neutral. Phase to phase connections are still available, of course. But current flow through ground is still not normal.
Which is a great thing - if you put a current transformer on the ground connection, you now have a high reliability mechanism to detect if the system is grounded. This is a standard feature on the power grid.
Now, lets say a high voltage power line has been broken and is laying on the ground. At 500 KV, there is definitely going to be some current flow through the earth. And as with all current flow, voltage drops when current flows across a resistance. Starting from the 500 KV at the end of the line, and reaching zero back at the nearest system ground connection, means that there can be a huge difference between one foot and the other in that vicinity. In the industry, we call this step voltage differential, and it can be lethal. It's the reason why you may have heard that you need to shuffle away from lightning strikes and power lines, rather than walk; that keeps your feet close to each other and prevents a current flow from leg to leg.
On the off chance that a line has been downed and grounded, the current flow will radiate away from the point of earth contact to whatever path is most favorable for current flow. If the topsoil is recently wet, it will tend to stay there. If everything around is fairly dry, there may not actually be much current flow at all, and it will radiate in nearly every direction as the voltage charges the ground. It will flow through ground water, if it can get there.
As far as the difference between AC and DC grounding events, the physical characteristics of DC make it more likely that it does not find a good path back to the nearest system ground, which makes it more likely to have a potentially lethal step voltage differential.
Best Answer
When electromechanical relays were still used, inverse time relays, definite time relays, and instantaneous relays were separate relays.
Modern protection relays combine inverse time, definite time, and instantaneous characteristics into one device. So you can have all three types in one device.
The difference between inverse time, definite time, and instantaneous relays
The time-current characteristic curve is different for inverse time, definite time, and instantaneous relays.
You can use combinations of curve types to achieve the design requirements. I commonly use inverse-time, definite-time, and instantaneous elements, all on the same relay.
Inverse time overcurrent relays: Slow to trip at low currents. Faster to trip at high fault currents. Used to co-ordinate over load protection, which may have a high starting current. Generally the most sensitive (lowest amps pickup), and slowest to operate.
Definite time relays: used to co-ordinate over other definite time, or instantaneous protection. Generally less sensitive (higher pickup) to prevent operating for load inrush. Generally faster operating time.
Instantaneous relays: Used when co-ordination is not required. Usually the least sensitive of all relays, as the relay must not operate for any kind of inrush, or operate before any downstream relay.
For more details, including application details, refer to:
Power systems protection is a deep and interesting field. Good luck!