I know they should be self-explanatory, but I'm not really clear on what is what. I'm buying a mountain bike soon, and I when I go into the bike store, I want to be clear on the type of riding I'll be doing.
There was a few threads about this a while back, maybe search a bit and read those.
Basically, XC is long rides where you don't do a whole lot of crazy stuff, mainly just trails with some obstacles and the hard XC trails will have a lot of climbs, some descents, rocky stuff, etc. Or just be insanely long.
Freeride, downhill are fairly similar for someone starting out, but downhill has racing and freeride for the most part doesn't.
Jumping, easy to imagine.
Trail riding is basically XC. Unless the trails are in town and follow along roads and you can ride them on a road bike, then its just city riding IMO.