As others have mentioned, cross country courses are fairly quick (a matter of a few minutes) at high speed, while endurance is done over the course of several hours at much lower speeds. Additionally, cross country is one of three phases of eventing/combined training (the other two are dressage and show jumping) There may be some competitions that are only cross country, but I've never seen them.
You could probably do some small jumps in a western saddle, so maybe you could initially begin with your current saddle (you'll start on tiny cross rails anyway!) but any jumping competition is going to require english tack.
One other thing to consider is that cross country jumps get very intimidating very quickly (to me at least) The first recognized eventing level is Beginner Novice at 2'7" and the jumps are very wide as well as tall, and are solid. Some shows have lower, unrecognized levels (I'm going to one this month at "intro" level, 2'3")
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon