@MHM here is a very basic summary of AERC endurance (how rides are run in the US and Canada)- There are several distances you can compete at 25 & 30 (which are called limited distance) 50, 55, 75, & 100. Each distance has it’s own amount of time you are allowed to be out on trail (25 miles= 6 hr time limit, 100 miles= 24 hr time limit, etc). Your horse is vetted in the night before the ride (pulse, hydration level, gut sounds, soundness plus a few other points). The ride itself consists of what is called loops or legs on marked trail. The loops can be the same but often aren’t and come back to camp where your horse must come in a certain pulse parameter, then will be evaluated by the vet and given a letter grade (like in school A is best) for the same things that were checked at the original vetting. Once a horse passes that (aka deemed fit to continue by the vet) they have a mandatory rest period where often the rider’s goal is to stuff as much food into their horse as possible to keep them fueled. Some rides go in a continual line or loop where these holds/ vet checks will be along the trail. These rides while they are technically a race (first person to cross the finish line, pulse down and vet in with a horse that is fit to continue is the winner) and can be competitive, are very much about taking care of your horse. I’ve never met more knowledgeable, encouraging and helpful people than fellow endurance riders. (note this is a very simplified version of a ride but at least you get the gist)
I can’t really talk to FEI that much other than to say the rules are slightly different and that FEI rides in the Middle East are very, very different from our rides and have had a lot of controversy surrounding them. These rides are flat track races for 100 miles- horses dying seems like no big deal, horses are switched, horses are chased by people in cars, etc. Right now there is a big movement to separate AERC from anything to do with the FEI rides. Again oversimplified but hope this helps explain
PS more experienced endurance folk- please feel free to make any additions or corrections to this