These are merely generalizations, and for the most part there are exceptions to all of these, but here it goes:
Dynamic speakers are the most common sort you find on the market. The basic design is a voice coil mounted in the center of a flexible cone structure; when the voice coil moves, the entire cone structure vibrates in common and thus, waves of sound are produced.
Horn speakers normally use a small voice coil, similar to dynamic drivers, but instead of a moving voice coil mounted to a flexible cone structure, the waves produced by the motion of the voice coil is amplified, megaphone style, out from a rigid horn shape structure. Horn speakers tend to be very high sensitivity/efficiency (requiring extremely small amounts of extremely clean/high quality power).
Planar speakers are based on ribbon technologies where a large array of conductive elements are laid out across a superlight membrane (oftentimes mylar) and they are set into motion by magnetic force. They operate in similar ways to electrostatic speakers, but do not require separate power sources to operate. Planar speakers are known for incredible speed, but also for low efficiency/high power draw. I am not 100% clear on the distinction between "true" ribbon and "quasiribbon" planar speakers, as produced by my favorite brand of planars, Magneplanar.
I happen to be using a pair of two-way dynamic loudspeakers, the Paradigm Studio/20
stereo loudspeakers; one day, though, I hope to buy a set of true ribbon, "Maggies," assuming I've a sufficiently matched front end and a room that would be appropriate.
I repeat, those are mere generalizations, and there are hundreds of thousands of variations on those mentioned above as well as even more types I've not even mentioned.
PS I've yet to listen to true ribbon planars, horn speakers, electrostatic headphones or in-ear headphones; I sure would love to, though!