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?

You can also make hard drive heads play music. Poor quality music, but music.

Multiple piezoelectric buzzers could probably play a tune if you tune them to individual notes. Not sure how to tune them, but probably cutting them, or putting bluetak on them would alter their note.