ESP incorporates everything that exists in ASR. I believe ASR is Mercedes-Benz's term for what everyone else calls traction control. All traction control does is reduce wheel spin by cutting engine power. What ESP does is make sure that the vehicle stays in its intended path. So that means that, apparently from the way your ESP works, it will let the wheels spin as long as it is able to keep the car in its intended path - which is straight in your case. ESP is the only system on a car that has the ability to apply individual brakes, thereby preventing understeer and oversteer. So if the sensors feel like the car is still moving straight, they will not cut the power. However, even though you claim that the wheels continued to spin, maybe it was just one of the wheels that was spinning as ESP may have applied the brakes to the other one? I really don't know, but that's basically how ESP works vs. ASR. All ASR does is cut engine power to reduce wheel spin. It can't control oversteer or understeer. ESP can cut engine power and/or apply individual brakes.

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1999 Mercedes-Benz S600, 103K miles - garage queen
1988 Mercedes-Benz 560SEL, 89K miles - daily driver
2007 Hyundai Sonata Limited, 31K - daily driver