Here's the general idea... most divisions will have 2 flat (no jumping) classes, one judging your horse (hunter under saddle) and one judging you (equitation). Then you'll have at least 1 but probably a couple jumping classes judged on your horse (hunter I, hunter II, etc) and jumping class judged on you (equitation over fences).
As far as divisions go, most of the rated shows will have the same names but there is a bit of variety among the schooling shows! You'll need to call the barn hosting the show and request what's called the 'prize list', or more likely your trainer should have one from them. Or they'll be there at the show office when you fill out your entry form. It's basically a small booklet that has the entry form, a schedule of the show, and a list of the levels/requirements for each division. Here our basic schooling show goes like this:
Short Stirrup-18 in for riders under 10 y/o
Long Stirrup- 18 in for riders over 10
2"3 Very Low- 2"3 but open to professionals
3" Low- 3" open to professionals
I've seen prize lists that have a 2" class, crossbars (12in), mini stirrup (like leadline), and rusty stirrup (riders who are... a little more vintage
And then jumper classes. But in some states short/long stirrup classes are 2"3! So you might have to ask your trainer or call around. Good luck!