Electromagnetic Torque is the torque produced in induction machines. It is the product of time varying electromagnetic field due to time varying voltage or motion of the rotor with the stator as the reference.
Synchronous Torque is the torque obtained due to the interaction of a time varying field based in the stator and a stationary field in the windings and the field poles of the rotor as in a synchronous machine.
Reluctance Torque is the torque seen in machines such as the reluctance motor. Here, the torque as the rotor shifts to align its minimum reluctance path with the rotating air gap which varies with time.