let's write a descent explanation, starting with the baiscs.
when a car is moving, all wheels turn. if the car makes a turn, the inner wheels has to move less distance than the outher wheels. this is why a differential is for, all the movement the inner wheel doesn't make, the outher wheels make in addition.
a diff looks sth like this:
now we get to a problem. imagine you're offroading, you hit a rock, and your right wheel doesn't hit the soil no more. you'll push the throttle, the right wheel will spin like idle, and the left one won't move at all, neither will your car.
to solve this they've invented limited slip differentials.
the most simple one, works with springs and clutches. if one wheel starts spinning significantly faster than the other, the clutch is engaged, and the other wheel is dragged along.
the torsen idleTask was talking about, has it's own gearbox you can say. if it's created with a ratio of 1:5, it can split it's torque giving 5 times as much to the wheel which has the grip, traction. (this is what audi quattro has)
the viscous coupling i pointed at, is primarily used on 4x4 vehicles to devide power between front and rear. you can pretty much compare it with a torque converter. the faster the rear wheels are turning, the more torque there is provided to the front wheels.
the limited slip differentials are sometimes also called locking diffs. this is a very confusing name caus there is nothing actually locking. some diffs have the ability to lock, but this addition can be put on all sorts of diffs. and shouldn't be used except for sever, slow off-roading
these systems are all normal diffs, they're all mechanical components and react due to a spring or sth like that. an active diff on the other hand, is hooked up to a computer, and uses several sensors to calculate what the optimal reaction would be. this is what the skyline, EVO, S60R, ... have
the impact of LSD is sometimes also achieved through EDL (no idea what it stands for). this uses the ABS sensors. these not only check if one wheel is blocked, they also can recognize if one wheel is turning faster than the other. if it does, it engages the brake at the faster spinning wheel, so the other can catch up. as you can figure this trashes handling