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2wd vs 4wd
The usual type of stock differential is an open differential, a simple arrangement that is inexpensive and works well on surfaces with sufficient traction. The problem is that when traction is not always sufficient; in those situations one tire spins, one tire is stationary, and the vehicle is stuck.
One way to meet this challenge is to use a locking differential (LD). A locker can be changed, electronically or by air pressure, between two states:
Another way to meet the challenge is to use a limited slip differential (LSD), whether physical or virtual. A physical or traditional LSD uses clutch packs or worm gears to limit the difference between wheel speeds. A certain amount of spinning of one wheel relative to the other results in a clamping effect which can either lock them together (practially speaking) or limit the difference, as in a torsen type LSD.
The sensors and controls associated with ABS brakes allow for virtual forms of limited slip. A subset of Electronic Traction Control (ETC), Brake-lock differential (BLD) can control wheelspin with an otherwise-open diff by selectively braking the wheel that is spinning. In addition to stability controls that will not be addressed here, many ETC systems can be configured on the fly: