DW. Yes, you got it.
The wiki article here is worth a read.
https://en.wikipedia.org/wiki/Unive...sal motors can be and,can go over 20,000 RPM.It actually mentions thyristor speed control part way down. The triac speed controls we have been talking about are equivalent devices. They are used to switch AC power on an off rather than DC.
Small universal motors spin fast and are geared down in many tools. One of the fastest applications is a router or a dremel type tool where the motor speed is the spindle speed - 18,000 maybe 22,000 rpm.
A brushed motor will typically make at least one full revolution, often 2 or even 3 revs in just one half cycle of the mains. Ie the voltage going from zero to peak and back to zero.
Speed control by switching off part of the half cycle just means there is no "push" for part of a revolution or a part of every 2nd or 3rd rev.
Inertia keeps the motor spinning during this break but the current is interrupted, the heat in the motor coils is reduced and the overall result IS equivalent to turning down the voltage over the whole AC waveform.
Raffo is right that the motor will still see a 120V max at the peak of the cycle but that won't hurt it. It's the heating effect of having too high an RMS average current pushed through it that has to be reduced.
It won't be in the next few days but if you want and you remind me, i'll connect a 'scope and a volt meter to one of these speed controls and take some photos with a power tool plugged in. I have one kicking about. I'll plug my ELU MFF80 plane into it and you can see what happens. Only 850 Watts but it's one of the most kick *** powertools I have.