This is the noobiest question… I’m looking to begin training my horse to jump. I’m a total western rider but I like both disciplines. I’ve heard Hunters are more “correct” on form and care about their positioning. Show is more of jump as high as you can. No offense to either, because I have no clue.
Hunters are judged on style and way of going. “Correctness” is relative to the discipline (as with all judging) - a winning show hunter snaps both knees up evenly, arcs its back over the jump (“bascule”), and travels between the jump in a smooth way on a particular length of stride between the jumps. Leads matter, flying changes matter, and behavior matters.
Jumpers are judged on whether they go around the course cleanly (without “lowering the height of the jump” by knocking down a rail) and within the time allowed by the course designer. Objective judging instead of subjective judging. Style and behavior does not matter for placings, but don’t mistake that for a lack of correctness! Showjumping is highly technical.
If you are new to jumping, you should plan to take lessons and work with a trainer for a substantial period of time before attempting to train a horse to jump.
ETA - welcome!
I just want to add - there is no discipline called “Hunter jumper.” Hunter/Jumper shows are called such because they have Hunter classes and Jumper classes.
Each include a range of class types. Hunter Over Fences are your jump classes judged with the Hunter criteria Redlei described. Hunter Under Saddle are your flat classes. Hunt Seat Equitation are Equitation classes (where the rider is judged on style, correctness, accuracy, and effectiveness, can be over fences and on the flat). Then you can also have Hunter Classics and Hunter Derbies.
Jumpers at many (most?) shows include an initial round, where all of the riders in the class complete the first round, then those that went clear (including within time) go back to do the jump off. Another format has each rider jump the first round, then if they went clear they stay in the ring and do the jump off right away. Power and speed is where a “single” course is split into two phases. Each rider does the first phase, power, and if they’re clear they immediately complete the speed phase without stopping between the phases. There’s a few other less common formats, such as six-bar competitions and Jumper Derbies.
All class types are available in a variety of jump heights depending on the show. Local schooling shows will often start as low as ground poles, crossrails, 18", etc. There’s 2’ hunters, 2’ jumpers, etc. Jumper classes at the higher levels are larger fences, going up to 5’3’’, (5’6’’+ in six-bars). Hunters usually top out around 4’6’’ at the highest levels, 3’6’’-3’9’’ at many small local shows.
You aren’t judged on rider form in jumpers but you need to be a good rider. The jumper courses are more complex and more technical than hunter courses at the same level. And faster.
Jumper riders are more pragmatic. Hunter riders can get caught up in some style over function habits. Jumper is all function.
Go to some shows or watch some videos online and see which appeals to you.
Note that hunters also judge the total impression and way of going of the horse. There’s a pretty narrow range of “good hunter type.”
On the other hand, at the beginner and local levels people do both, it’s easy enough to swap and a slower simpler hunter course might be good for a beginner.
Go get started at a barn that does both, and see which you gravitate towards. Both are very technical, but in different ways.