Post grad intern, Contractor & then?

It typically has more to do with an HR classification. It is easier to get an additional intern through a lot of systems than it is to get a contractor. A contractor typically has to be justified on a per project basis, while and intern you can justify more easily as extra help. A good place will pay you in their contractor pay range vs their student intern pay range. I think you can safely list it on your resume as contract work because that is what it is.