I don't know if its the same in the jumpers, but I did an adult medal hunter class and it was basically judging the rider over a hunter course with some extra tests like bending lines and trot fences. Then the top 10 came back for a flat class. I only did a 2'6 medal class though at one of the local shows once, so I could be way off, but thats the way my coach explained it to me - like an equitation class.
I think that it's pretty much an equitation class but with jumper jumpers, sometimes a more jumper type course and in jumper apparel. you'll still be judged but there was also a time allowed when I did one so you needed to stay under that or would be penalized.
A jumper medal is a judged class ridden under jumper rules. If it's in two phases, one will be the jumper round and the second will be flat with the combined score determining the overall placing. Your prize list should outline the class or division for you.
As far as I know, awards given depending on how many classes, divisions, and shows you participate in in a given year is something entirely separate. I never competed enough to qualify, but around here it's a gala at the end of the season where they give out different awards corresponding to division and performance.
The rules say jumper tack - what about the saddle pad?
In jumper medals such as the WIHS jumper phase and USET Talent Search, you will usually see a regular hunter saddle pad, and occasionally a white square pad. I'd stick to a hunter shaped pad, figure 8 if you want/need one, and a running martingale.