Most pool pumps can't handle the electrical noise coming out of the less expensive variable speed controllers, i.e. they are “noninverter-duty”. Depending on the speed controller it might have something to clean up the waveform so it is compatible.
My understanding is that most pool motors are single phase, with a starting coil. In this case, there are very few AC motor speed controllers that will work, because most speed controllers are designed for 3P motors. There are some rare 1P/1P AC speed controllers, but they are quite expensive, esp. for 1 1/2 motors. If you ran a 1P motor off a 3P output speed controller, the motor won't start properly (or it will start in reverse direction), or it will just sit there and buzz until it burns out the coils. You can purchase 3P motors to connect to the wet-end of your pump, but these are a bit expensive, esp. as the HP increases. A new 1P or 2P to 3P speed controller will run about $200-300 off of eBay, btw. These speed controllers alter the frequency going to the motor to control the speed. They can also do some PWM to reduce the voltage, but they need to vary the frequency to run the motor at a set speed. I believe 2 speed single phase motors simply double the amount of coil to run at 1/2 speed, so switching between full speed and 1/2 speed means applying current to more wire in the motor. This is not the same thing as a speed controller, obviously. I have a WhisperFlo to control our waterfall, and I would love to be able to throw a speed controller on it to turn down flow, but to do so would be almost as expensive as buying another IntelliFlo, which doesn't seem worth it to me.