What is the name of the drill that is to remove the lugs off the wheel of the car?

I think you're talking about an impact wrench.

Or it could just be a drill with a socket adapter, but most drills don't have the torque required to do this without someone getting it started first with a lug wrench or something.

An impact wrench is basically a drill with a sort of transmission device. The drill shaft rotates freely intially to build up momentum and then the transmission engages to deliver a lot of torque all at once. Impact wrenches tend to make a characteristic "rattling" sound as the transmission engages and disengages.