Not much more I can say about hunter vs jumping but I will add that hunters generally ride more out of their tack and in a half seat. This allows the horse/pony's movement to be judged more. Just to add and make it a little more confusing there is Equatation or Eq which is based on the rider. The jumps are generally more colorfully and the horses are ridden in more of a frame. The courses are also more challenging with rollbacks, slices, bending lines, combinations, etc. Hunter courses are generally just outside line to diagonal line to outside line to diagonal line. My trainer has all of his kids do both divisions and are lessons are always "Equey" courses so when we do the hunter stuff its really easy!
Short Stirrup or "SS" is great for beginners. All the girls at my barn start with SS or Long Stirrup. The jumps may not be higher then 18 inches. At most barns they are just x-rails and at finals they are verticals. There is normally a hunter an eq division with in the SS division.
I wen to a show this past weekend and it had the cutest white small pony with a mohawk mane. The girl was like 6 and had HUGE pink bows. She rode really well and placed great. It was the cutest thing to watch! She had this huge grin the whole time! :)