Difference In Working
Synchronous motor: Stator poles rotate at the synchronous speed (Ns) when fed with a three phase supply. The rotor is fed with a DC supply. The rotor needs to be rotated at a speed near to the synchronous speed during starting. If done so, the rotor poles get magnetically coupled with the rotating stator poles, and thus the rotor starts rotating at the synchronous speed.
Synchronous motor always runs at a speed equal to its synchronous speed.
i.e. Actual speed = Synchronous speed
or N = Ns = 120f/P
Learn more about working of a synchronous motor here.
Induction motor: When the stator is fed with two or three phase AC supply, a Rotating Magnetic Field (RMF) is produced. The relative speed between stator's rotating magnetic field and the rotor will cause an induced current in the rotor conductors. The rotor current gives rise to the rotor flux. According to Lenz's law, the direction of this induced current is such that it will tend to oppose the cause of its production, i.e. relative speed between stator's RMF and the rotor. Thus, the rotor will try to catch up with the RMF and reduce the relative speed.
Induction motor always runs at a speed which is less than the synchronous speed.
i.e. N < Ns
Learn more about working of induction motor here.