ID is Irish Draft, which is a breed. TB is Thoroughbred.
A hunter would be a type of horse that could be used for hunting. A good hunter would be around 16hh, and can be lightweight (fairly finely built), mediumweight (bit heavier) or heavyweight (pretty hefty). They have a different conformation from cobs, which tend to be well built and stocky, with short legs, good deep girth, and good quarters and shoulders. Hunters are a bit taller and rangier, longer in the neck and leg and wouldn't have the same movement.
Then there's hacks... hacks are a kind of lightweight riding horse - they must have very correct conformation, and they're usually TB or TB crosses. They're much lighter and usually smaller than hunters - not so plain to look at either. Where a hunter might get away with a small blemish in a hunter class, a hack certainly wouldn't.
A hunter can be a horse of any breed really that conforms to that type. A 16hh Welsh cob might, or a heavier TB, and ID cross - as long as they are the right type. They should be trimmed (feathers clipped off if they have them, manes and tails pulled and so on). A hack would be trimmed in the same way but might also have 'quarter marks' - that is aptterns brushed into the hair on the quarters. Hacks are plaited for showing. Cobs have their tails pulled and feathers and manes clipped off for show cob classes, or can be shown with full manes and feathers in traditional cob classes (gypsy cobs are sometimes shown like this).
