Yeah, 'Generator' is a generic term really - a device to convert one type of power, usually mechanical, into electrical power. The generators in old cars had brushes and commutators to give a direct (ish) current output, smoothed by connection in parallel with the battery. The alternator in your modern car is externally excited, and has a regulator and diode pack built in to give a DC (ish) output. Alternators generate 3 phases of output, 120 degrees apart, the old car type DC generators only had 1 phase, (I think), hence why alternators can give a much larger output.
All electrical power on any aircraft originates from the 'generator(s)' or the battery(s). AC from the generators/alternators is converted to DC for various systems, those DC systems being capable of being supplied by just the batteries in the event of generation failure, as an emergency back-up.
Edit: smilin_Ed, I guess your reply arrived while I was writing mine !