In simple, synchronous generator supply’s both active and reactive power but asynchronous generator(induction generator) supply’s only active power and observe reactive power for magnetizing.This type of generators are used in windmills.
Synchronous generators (otherwise called alternators)are three phase generates, which have a rotating field, and a stationary armature where emf induces ( armature can be rotating, but usually not using practically. ). Here the field rotates to get a varying field and the stationary armature places around it to cut the flux and EMF induces in it.There is no other case of motoring until the current direction reverses and at synchronous speed. The setup is called as synchronous generator because it work in sync to some other generator or a system. So in the whole system, each module should keep some standards ( like frequency , terminal voltage, etc…).