Original: In an automobile, the compressor is driven by a belt over a pulley, the belt being driven by the engine's crankshaft (similar to the driving of the pulleys for the alternator, power steering, etc.). Whether in a car or building, both use electric fan motors for air circulation.
Simplified: In an automobile the compressor is driven by a pulley on the engine's crankshaft, with both using electric motors for air circulation.