there are many kinds of motors. go to wikipedia.org and look up the word motor or go to encyclopedia britannica (even better).
off the top of my head, the ones I am interested in the most are:
[DC or AC] brush motors,[DC or AC] brushless motors, stepper motors, linear stepper motors,
they come in all sorts of drive configurations depending on your need. some have built-in drive circuitry or controllers.
linear step motors are used for moving tables in x-y or x or y directions.
motors are used in inkjet printers to move the print head, and in some types of laser printers to rotate the mirror for the laser to reflect off of.