boiling just makes the water move, hydro just cheats

Electromagnetic induction.

Basically electric motor in reverse...instead of electricity powering the motor, the motor powers electricity.

But the trick is in "what spins the motor". In the case if ICE generators, it's usually a pulley off the crankshaft.

Or it could be moving water.

gas generators based on internal combustion

they heat air, afaik. hot gas expands -> mechanical movement moves magnets -> electromagnetism -> electric power.