As far as I know traction control is a very basic form of ASR they operate in different ways. Traction control is easily implemented on any car with ABS by using the ABS sensors to measure wheel speed it is possible to detect a wheel breaking traction and reduce the power to the driven wheels to restore traction.
In a normal car with no limited slip differential the power will go to the wheel with the least amount of grip and that wheel will spin. If you try to pull away with one wheel on ice and one on tarmac the power will go to the wheel with no grip spinning that wheel meaning you don't accelerate.
ASR works by applying the brake to the wheel that is spinning and this means some power is then passed to the wheel that has grip meaning you are able to accelerate.Very useful at slow speed.
So ASR is advanced Traction control using EDL (Electronic Diff Lock).
It also works at high speed but it depends on whether both driven wheels are spinning or one is spinning on what it decides to do.
The following is from
http://www.italiaspeed.com/new_models/2 ... /safe.html
ASR (Anti Slip Regulation)
ASR (Anti Slip Regulation) is also built into the ESP system, optimising traction at all speeds, assisted by the brakes and the engine control.
The device monitors the wheel speed calculated by the ABS sensors to establish the amount of slip and triggers two different control systems to recover grip. When an excessive demand for power causes both drive wheels to slip (for example, aquaplaning or accelerating on an uneven, snow-covered or icy road surface), the system reduces engine torque by decreasing the throttle valve aperture and thus the air flow. If, on the other hand, only one wheel slips (for example the wheel on the inside of the bend, after acceleration or a dynamic change in the load), this wheel is automatically braked without the driver having to touch the brake pedal. The effect is similar to that of a self-locking differential. This gets the Grande Punto out of any difficulties on surfaces where grip is poor.
ASR is engaged automatically every time the engine is started, but can be excluded by a pushbutton on the central console. ASR must be excluded when snow chains are fitted because in this case, in order to transmit torque to the ground, the wheel needs to be able to 'accumulate' the snow, with small slips that the ASR tends to avoid.