'Traction control' as commonly used when describing a vehicle seems to refer to a system which senses wheel slip, and in an attempt to assure vehicle control they modulate braking and/or applied power. One symptom would be mashing the throttle when on ice with poor tires for the situation, having little wheel slip, the vehicle stays pointed in the right direction, but you don't go anywhere :^)
It's seems to be more sophisticated than but a complement to ABS, which modulates braking based on wheel slip in an attempt to maintain vehicle control. A symptom would be mashing the brakes when on ice with poor tires for the situation, having little whweel slip, the vehicle stays pointed in the right direction, but you don't stop :^) A friend was 'comforted' by the ABS light in his truck blinking at him as slid thru a stop sign, but he said that at least he was pointed in the right direction.
Common systems which transfer power from a wheel with with low or no traction to one with some traction are limited slip or locking diffs, selectable or otherwise. These typically increase torque to the wheel with traction, and a common sympton on uniformly low traction surfaces is the rear end breaking loose, as both wheels were already on the verge of breaking loose. Another symptom of a limited slip is being on uneven surface with a 4wd and a front and rear wheel off of the ground, and not going anywhere, as a limited transfers a portion of torque to the wheel with traction, but a portion of zero is zero. Some of these systems can be made to engage a bit with braking.
AWD seems to typically refer to systems which allow some slippage in order to prevent binding, which is why they don't work well for handling heavy loads.
Some systems have diffs front and rear as well as a center diff, others have just a transfer case with front and rear diffs.