There are two different forms of Rugby, with varying rules.
Rugby Union is what the All Blacks and Wallabies play, and is bigger as an intenational game than it is domestic. Rugby League is the bigger national game, but is also played internationally.
The US is actually getting into Aussie Rules (but it needs a new name) in an official way, with actual teams being fielded, and hopes to compete on an equal level with Oz. I can't wait. I'm sick of the Aussies gloating because they thrash an adhoc team of GridIron players who don't know the rules or what they are doing because they've never played the damn game before.