We are talking about single-phase motors.
For single phase AC, there are only two types of motors:
Squirrel cage induction,
and series wound universal, where both the rotor and stator have windings.
For polyphase motors, there are other variants like wound rotor induction (not to be confused with a series wound universal) or synchronous.
Regardless whether it is wound rotor or squirrel cage, all induction motors should be operated at a constant volt/hertz ratio to prevent magnetic saturation. Therefore, if a motor nameplate lists 240V/50Hz, to reduce its speed in half, one would apply 25 Hz, but the voltage would have to be reduced to 120 volts.