There is some integration between the two apps. I'm not sure how much. I know it is possible to export iPad Garage Band files to the Mac version, but I'm not sure it will work the other way, as the Mac version is considerably more capable feature wise. You'll have to ask some people who do this (there is a Musician's area somewhere eon the forum) for details.
While iOS and OS X share some things in common, but they are not compatible app wise. There are several reasons why this is a good idea, at least most of the time. The biggest being that attempting to make them compatible would have made iOS a bear to fit on a device like the iPad, and the code needed to make the same app run on both would have be oversized as well. It is going to make it run pretty, anyway, and Apple doesn't care much for making things that run ugly.