They aren't part of the North. They have their own culture, different gods, different kings. They often raid the North, and they are closest to hte North, which is why the North went over to kick them down when they rebelled. But they aren't part of the North.

In the past, their kingdom was, at times, much bigger than just the isles. See Harren and the Riverlands. But I think it was said that other kings of the isles had, at times, conquered other rivers and coasts.