Following a thread started by BeeCurious
, I salvaged discarded treadmills to gather motors with plans to build an extractor. Treadmill motors vary, but one I like has an electronic speed control, circuit board & transformer that resembles the photos above. Along with the variable speed, while the treadmill didn't go in reverse, as the motor is a DC motor it is easily capable of reverse by reversing the two wires (or adding a switch to do so).
Another treadmill I salvaged has a single-speed AC motor and a mechanical variable speed (diameter) pulley to adjust the speed. A simple design, but for the treadmill user it means they have to stop the treadmill and go to where the motor is mounted to adjust the speed.
Capacitor start AC motors are more difficult/expensive to make variable speed, AFAIK. The modern way to have variable speed with an efficient AC motor is to use an inverter to provide variable frequency AC to the motor, but for an older extractor it seems unlikely that approach was chosen.
So the circuit board and electronic variable speed in the photos are clues (from my perspective) that the extractor motor is likely DC.