You can use bell boots when jumping and they won't get in the way. You can use any kind of protective boot for schooling at home--splint boots, polos--but open-front jumping boots are good for schooling, too, and you can use them in the jumper ring but you can't use them in the hunters. Open-front jumping boots give the horse protection and support but the front just has the straps so as to allow the horse more clearance from the jump.
Opportunity is missed by most people because it is dressed in overalls and looks like work. ~Thomas Edison
Well, open fronts are designed that if the horse hits the jump, they'll feel it, and lift their feet up higher next time (or that's the purpose). I use splint boots (on Sun), but I prefer using open fronts and bell boots. For cross country, I prefer brushing boots with bell boots. But for hunters, you can not use boots.