Different amperage with a normal and a hook Multimeter?
AC circuit behavior is much different from DC. AC circuits have impedance rather than ordinary resistance. Impedance includes both resistance and inductive or capacitive reactance. An ohmmeter measures only the resistance.

In addition, power in an AC circuit is voltage X current x power factor. Power factor is a number between 0 and 1 that accounts for the effect of the phase relationship between voltage and current.

In addition, motor current is mostly determined by the load. In an AC motor, the load is like a variable resistance that is infinite when the motor is not running. When the motor is running the load resistance appears to be connected in parallel with the fixed internal resistance and reactance of the motor.

In a DC motor, the load is like a generator inside the motor that has a variable voltage that opposes the supply voltage. The opposing voltage is usually called "back EMF" (reverse polarity electromotive force).

The above is a simplification that attempts to present the general idea. You will need to study the subject in detail to really understand it.