So, my experience can chip in too!
Lets start with the most common - jumping boots. These are usually Tendon boots and fetlock boots. They are soft on the inside, can be lined with sheep skin, usually velcro for closing, but can be different straps too. The outside is harder plastic material, it protects the horses leg against hitting the poles and so on. However, I always wondered, why do they not cover the front of the leg - that is what usually hits the pole and it falls. Some explained that it is only tendons that need protecting, however bones can bruise too, but apparently horses learn to lift their legs if they hit them a few times.
These boots are quite often used in flat-work as well, especially for horses who do not go clean, hit their feet together etc. I know a gelding who used to be a trotting noise maker. When he used to trot, and you got him forward enough, you heard the fetlock boots clicking together, his back hoof hitting the front shot etc etc. He was wearing tendon boots, fetlock boots and all 4 bell boots.
Bell boots as explained protect the back side of the hoof, help with not losing shoes, even though some horses still lose them
I know a gelding who used to wear back on track stable bandages, more like wraps with 4 Velcro straps, He had sensitive legs and was living in an outside box, the ground used to freeze in his box, so they decided he needs those. He was a much happier horse after he got them.
I have seen other horses use stable wraps even in summer. Not quite sure why, owners never explained, but we had to put them on for the night mostly. One horse had a bad leg and needed the warmth.
For going outside they used something similar to (at the moment the only I can find) horse work boots or horze prosoft boots - they are a lot softer, warmer material, similar for all 4 legs. We used to put those on for both training for some horses and also going to the paddocks.
Polo wraps - that's a completely another story. Some might use them at every lesson, some just in winter, some don't use them at all. They are most commonly used to help warm up the legs better for work, sometimes for stability, most commonly to wrap up for an injury. I personally use them occasionally on trail rides, they give minimal support but still, if we step wrong somewhere or brush against fallen branches or trees. And they can help in snow to protect against the crust cutting the leg. That is mainly for stabled horses who don't even grow enough fur for winter.
Transport boots - can be used only in chilly weather, in hot summer the legs will basically roast. Some horses will get bandages or tendon boots on for transport in summer instead of the big transport boots.
I think that's all I can chip in with now.