Source voltage really doesn't have anything to do with it, outside of the fact that if you don't have a power supply to step up voltages, you will be limited on the output power. The power supply in the amp will step up voltages to meet the requirements of the output devices on the rail. If it's on 120V AC, then it's stepped down and taken to DC to meet the same requirement. It's about the output device topology, not source voltage.Just think about Ohm's Law in its entirety, but with the limitations of a using 12VDC power supply.
For a basic primer on auto audio electronics, visit here;
Basic Car Audio Electronics