Rugby League and Rugby Union. I have no idea what the difference is. A quick search unearthed the following article, amongst the usual Wikipedia and Yahoo Answers crap:
http://www.bbc.com/sport/rugby-union/25124313
Former Iowa Rugby player here to help. There's actually now three forms with Rugby 7s (7 man teams instead of 13, coming to the Olympics). Think of it like an evolutionary chain: soccer-->rugby union-->rugby league-->football. Hence, rugby league is more like football, with a certain amount of downs before it turns over to the other team (so it is often kicked to them on the last down) and the ball is reset after a tackle which leads to faster, open-field tackles. Rugby Union is closer to soccer in that one team can have the ball as long as they can keep it, and play is not re-set after a tackle. Rugby Union is more popular worldwide, with Rugby League being bigger in the Southern Hemisphere. Don't know if any of that helps.
As always when I talk about this, I have to say that we have a great college rugby program in our own back yard. Iowa ended the 2014-15 season ranked #20 in rugby union and #12 in 7s (after a great run in the national tournament). You all should go out and check them out at least once.