You can power a motor directly from a AC or DC source, it is done all the time. A desk fan you power from a out less it is unlikely to have a driver. A battery power fan can just have the motor connected to the battery via a switch to turn it on and off.
You can regulate the speed of a DC motor speed with a potentiometer, It is just a very inefficient way to do it. Triac designs like power tools uses are a lot more efficient.
All motors that result in continuous rotation are really AC motors. A motor with DC input has brushes and a commutator that physically changes how the coils are connected to the input. So mechanical AC generation. A drawback of this is the brushes can wear out
A brushless DC motor is really an AC motor with a driver that has DC input. The output to the motor is AC so the commutator and brushes are no longer required. The advantage is no brushes that wear out, and the torque and speed are also higher for a motor of the same size
If you want to control the speed of an AC motor you need a driver that changes the frequency. Today they work just like the controller of a brushless DC motor, the difference is just you need a rectifier at the input to create the DC the electronics used to produce the AC that you can change the frequency of.
So if the motor needs a driver or not depends on how you intend to use it and what type if motor and power input you have.
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