I'm an American as well living in Tasmania for the year, and have been watching both now for a while, and loving it. There is a hug difference between Rugby and Aussie Rules.
1) Rugby is mostly a bunch of fat guys running two metres (yards) and then getting hammered, and then they do the same thing like 4 more times and the other team gets the ball.
Aussie Rules is much more involved and interesting, there is much more movement, and takes a lot more skill. Basically in Aussie Rules you have 18 players from each side, spread out over an enomous oval. You have to kick the ball to eachother or hand pass (dont ask me to explain its really confusing). If you kick the ball over 15 metres (15 yards or so) and someone catches the ball they get to stop play and no one can tackle them, if they drop the ball they have an enormous fight over it. Also if a player runs for over 15 metres (yet again 15 yards) they have to bounce the ball, not unlike basketball, except much harder.
2) In rugby the game is more like Gridiron Football (thats what aussies call American Football) you have to get the ball into an endzone and touch the ball to the ground while u are still holding it. Then you get to take a kick to get an extra point (except its much harder because deepending on where the ball is touched on the ground in the endzone, is where u have to take the kick from).
In Aussie rules there are 4 poles at each end of the oval the two in the middle are much higher then the two on the ends...if you kick the ball through the middle uprights u get 6 points, if you kick the ball and hit the post or get it through the side posts you get one point.
Thats all for now, hope that helps