A hunter is more workmanlike than a riding horse, a riding horse is between a hack and a hunter in type usually more TB blood.
You would wear a coloured browband with a riding horse, plain with a hunter.
Found this that might help
Hack - was "the horse to be seen on" - flashy, with impeccable manners and balance. Fine TBs who ooze elegance.
Riding horse - The more practical alternative to the hack - has more substance and less flash, but still an attractive horse who should turn heads.
Hunters - this horse should be a quality stamp, good substance, good amount of bone. Basically a horse who would hunt - attractive but not flashy. Well mannered and must must must gallop!