I would say not 'nonexistent', but rather 'avoidable'; or, even better, that there is an isomorphism in an appropriate sense. (Compare the situation for strings and lists of characters; the types are isomorphic, but I wouldn't say that the difference between them is non-existent!)

True. I'm just a lazy relativist though ;)

Yeah, but I find that -- like dimensional analysis -- keeping careful track of what's upstairs and downstairs can help me keep a computation from going off the rails.