Well, first of all, brakes are individually applied by the system on all four wheels, not just the driving wheels. Second, the system actually monitors the motion and attitude of the car (vehicle speed, individual wheel speeds, yaw rate etc.) while comparing it against position of the steering wheel. Conventional traction control only analyzes forces longitudal to the vehicle's long axis; full stability control also considers the lateral forces. In other words, traction control is only part of the stability system.
I see. Traction control seems to be most helpful (my car has it) in the snow where the function of transferring power from the spinning wheel to the one with grip can keep the car from getting stuck.
In fact, last winter my driveway with a slight uphill incline had 2 or 3 inches of snow on it, I had no problem driving up it. The traction control was working quite a bit when I did that.