Synchronous machines are AC machines that have a field
circuit supplied by an external DC source.
In a synchronous generator, a DC current is applied to the rotor winding
producing a rotor magnetic field. The rotor is then turned by external means
producing a rotating magnetic field, which induces a 3-phase voltage within
the stator winding.
In a synchronous motor, a 3-phase set of stator currents produces a
rotating magnetic field causing the rotor magnetic field to align with it. The
rotor magnetic field is produced by a DC current applied to the rotor
winding.
Field windings are the windings producing the main magnetic field (rotor
windings for synchronous machines); armature windings are the windings
where the main voltage is induced (stator windings for synchronous
machines).