Traction control (TC) is designed to maximize the longitudinal traction of the tires by preventing excessive tire spinning. In other words, it monitors wheel slip and will apply brakes/reduce engine power when slippage occurs.
Stability control (DSC in BMW terms) adds lateral traction control to TC. It monitors the steering, yaw, and lateral acceleration of the car to control the rotation of the car. It "steers" the car by applying brakes at individual wheels.
People tend to mix up the two but they are NOT the same.