Meved he duscribing a motor speed controller
same Idea use on sewing nachines
These I know about that correspond to your description (triac dimmer like, just modified range) are smooth regulated with a pot, not with 2 or 3 fixed speed levels.
If the fan system had fixed 2 or 3 speed levels, all I've seen were actually 2-3 speed motor and a switch.
Using the triac dimmer with fixed 2 or 3 speeds makes not much sense, because such switch cost more than a pot it replaces in the circuit and offers less marketing value (few fixed speeds instead of smooth variable control). Plus the levels with triac dimmers tend to vary a lot, what would make the few speed levels very inconsistent. With a pot system this is masked just because the user can set anything from the minimum to maximum.