A synchronous motor runs at a speed which is synchronised to the frequency of the AC
voltage that supplies it. For example if the motor is supplied at a frequency of 60Hz then it will run at either 60, 30, 20 etc revs/second, depending on the number of magnetic poles (2, 4, 6 respectively) that it has (by design).
An asynchronous motor generally runs slower than the above with a speed that usually varies somewhat with the amount of mechanincal load that it is driving.