There are two main type of "Cell Phone Vibrators".
Linear Resonant Actuator (LRA) and Eccentric Rotating Mass (ERM)
LRAs are the newer, more efficient option—they use less power with a voice coil that vibrates a mass back and forth for better, more precise feedback.
ERMs are the old-school vibration motors everyone knows: basically an off-balance weight spinning on a motor for simple buzzes.