A hand mixer is the more modern version of an eggbeater mixer, but with a motor. A motor is encased in a top section, which has a handle . It’s the motor that moves the beaters, rather than cranking a handle.
Stand mixers have a frame that acts as the housing for a heavier-duty motor than a hand mixer, as well as the mounting base for a bowl, which is designed to fit the mixer and lock in place during mixing. They have various mixing attachments, which makes whipping, creaming, kneading, etc. an effortless task.