However, when you're giving advice out to strangers on the Internet, it's kinda alarming when you discover that you don't have common terminology.
Kinda of like describing to someone how to execute a complicated sailing maneuver, and at the end of the description, they say "Bow? That's the pointy end, right?" Suddenly you lose a lot of confidence that the person is going to correctly execute the maneuver, you know?
Some of this is undoubtably regional differences, I think in some parts of the country, the hunter/jumper as a sort of of general term is common. And if all your experience is with one barn or one trainer, you may have only limited exposure to how people refer to or describe things.
Good luck to you and the horse you're training.