You're right, there are a LOT of boots!
When people talk about 'hoof boots' IME, they're talking about protective boots that fit over the hoof and may or may not fasten around the fetlock. Typically they're used in place of shoes, or to help rehab an injured foot. Like these: http://www.renegadehoofboots.com/ima...talling-01.jpg
used for a horse that can't go barefoot over the terrain that they need to, but can't or owner prefers not to use steel shoes, or for a horse that has a medical issue that makes steel shoes a bad idea.
'Bell boots' are put around a horse's fetlock and hang over the hoof and heels to help keep a horse from accidentally stepping on themselves or a shoe, pulling it off and causing damage. They don't go under the foot at all though. Like these: http://www.theequinest.com/images/bell-boots.jpg
used for horses that over-reach or need special shoes that are more prone to getting stepped on and pulled.
Lots of others... hopefully others will chime in! The term 'medicine boots' confuses me- I can think of at least four different things that that term might refer to, and all of them different!