Usually it's not exactly a speaker, but it does involve a controlled moving diaphragm. In a piezoelectric buzzer, a current applied to the diaphragm causes it to oscillate, and the size and shape of the diaphragm determines the tone AFAIK.

It may be theoretically possible to engineer such a device into a rudimentary speaker. I mean, people have done it with Tesla coils and player pianos, so hey, anything is possible?

https://www.labdarna.com/en/understanding-piezo-buzzers-how-they-work-and-how-to-use-them-in-electronics-projects

They use piezo buzzers which work differently to most speakers. I would guess that the units used in smoke alarms and microwaves generally have integrated drivers that only operate at a single frequency. However, it is possible to drive piezo discs at different frequencies. Their ouput will always approximate a sound square wave though, so don't expect to be able to use them like a normal electrodynamic/ voice coil speaker to play arbitrary sounds.

I don't have any answers - but now I wonder if your idea would be easier when working with one of the fancier smoke detectors with voice alerts. Those have pre-recorded voice alerts that "speak" when an alert occurs, rather than beeping. Those pre-recorded messages must be stored somewhere in the smoke detector.

Beeps don't usually come from a speaker, no. You might find this old ELI5 about electronic sound interesting.