There are two basic types of generators:
Dynamo: The output comes from rotating coils connected to a commutator, (which is a rotating switch fixed on the end of the shaft), and excited by fixed field coils (or sometimes permanent magnets). It produces DC.
Alternator: The output is taken from fixed stator coils, excited by a rotating field coil. It produces AC, (usually 3 phase).
Two other variants of alternators are:
DC Alternator: Has a built in diode pack. It produces DC.
Magneto: The rotating field is provided by a permanent magnet.