Someone who used to sell alternators and engineer DC systems here:
"Generator" is both a generic term for anything that gets spun to generate electricity AND a specific term for a unit that uses the brushes to provide a DC output. This works by having the current generated in the rotating part of the unit (the rotor) and having contacts on the rotor spaced correctly to always have + and - on the same brushes. Advantage is this is a rugged setup that can stand a lot of abuse. Running the current through the brushes is a disadvantage because they spark, generating radio noise, and wear out. Also for mechanical reasons they have a lower maximum RPM that alternators. Generators also make fairly good DC motors if you feed power into them and vice-versa. This can be seen on any aircraft with a starter-generator. 24 volts into it spins the engine and the running engine causes it to produce 28 volts (24 volts batteries charge with 28 volts

) I used to fly a Cessna that had a starter-generator to fire up the PT-6 engine. This is also a danger for a piston engine airplane with the traditional car-type electric starter. If the starter does not disengage you now have a very powerful totally unregulated generator running
Alternator is in theory a word for generators that produce AC. In practice it is hardly ever used that way. What it usually means is a unit designed to produce DC using built in diodes. Alternators are superior in many ways to generators for engine-driven DC power. The spinning part of the alternator is the field that carries a small amount of DC to provide the magnetic field. Thus there is no large amount of current through the brushes and the contacts are not segmented, thus eliminating the sparking. The stator - fixed windings - is where the power comes from. Alternators can spin faster too, so they can be geared to spin faster than the engine and charge better at idle speed. It is very confusing because alternator=AC, but DC comes out of it. In almost all cases rectifiers internal to the case change the output to DC. An alternator cannot become a motor powered by a battery. The only way to make one become an electic motor would be to bypass the dioes and feed it with 3 phase AC.
It was LONG ago when I worked at Piedmont, but if memory serves the 727s and 737s did not have alternators as the word is commonly used. They had AC producing generators, battery chargers run from the AC bus, and the APU provided air to start the engines. The APU might have had a starter-generator, I remember starting them off the ship's battery when the generator cart had gone missing, but can't recall how I set up the switches after that.