I built a simple triac control to change speed of our wood stove fan. It drew little current from mains, being small. I believe it was the type known as a squirrel-cage motor. Evidently its speed is unrelated to AC frequency. It went fast or slow as I dialed the potentiometer.
The same for my window fan. I slow its speed by means of a step-down transformer.
And my opposite experience...
I tried to vary the speed of my reel-to-reel tape recorder by hooking up the triac controller directly to its motor. Evidently its speed is linked to AC frequency because it maintained the same speed as I reduced waveform On-time. Suddenly it stopped when power was insufficient. Then I increased waveform On-time and it started spinning at its designed speed.