Regular shows are u allowed to bring the horse u want to ride. For IEA u to go shows and u or ur train or draw a horse that u have never ridden and if u r jumping then u get 2 warm up fences and if u are doing a flat u have to just go into the ring. I believe they are judged the same.
IEA is catch riding, but you get a warmup fence or two in high school (for IHSA the college equivalent, there is no warm up). It is entirely based on equitation and there are only two classes: flat and fences, per division. I personally did IEA in high school and am having lots of fun doing IHSA at UC Davis