Working with iWork on Mac and iPad?

I have bought iWork or iOS for my daughter to work on school stuff on her iPad. However, for the somewhat more complex stuff, she should be able to move to the big iMac. Before buying the iWork suite for Mac, I have been looking in what is needed to set up a reasonable work flow for her. I can set up a WebDAV on our server easily enough, so setting up some sort of bareboned exchange of documents betwene iOS and Mac should work. But what I have not been able to find is information on the compability between the iOS and Mac versions of iWork.

I kind of assumed that applications with the same name (Pages, Numbers, Keynote, iWork) would be document-compatible even if the iOS versions of the apps might offer a different subset of functionalities. But I get the feeling they are not compatible. Are they?