[Matt Adams]

I would group them as:

Stepper
Brush Servo
Brushless Servo
Induction Motors

A stepper drive applies DC voltage to alternating phases in the stator of the motor, stepping it along. If you apply DC voltage to any 1 winding, you'll either move one step or apply holding torque and position will stay.

A brush servo is applied DC voltage, and its speed is adjusted through PWM modulation which effectively raises or lowers the voltage. If you apply DC voltage, the motor will spin.

A brushless servo also has DC voltage applied, but is applied sinusoidally between phases based on the rotor's position relative to the stator. If you apply DC voltage between any two windings, the motor will move to a pole and stay there.

An AC Motor, is also brushless, but its speed is based on the frequency of the AC voltage supplied by the VFD, and all three phases are applied. If you apply 3 phase AC voltage to an AC motor, it will spin based on the frequency of the voltage.

Hope this makes sense,

Matt