I think that first 'all' shouldn't be there, right? That is, these are all possible orders of vector fields and differential forms (among which the various Hodge dualities permit lots of identifications) on submanifolds of ℝ^n, but they're not all the possible particular cases of such vector fields and differential forms, in the sense that there are plenty of other, different physical situations that lead to the same mathematics (which, as you argue, is why the concept is so useful).