Resawing is a type of rip cut (always, without exception). The reason for the different terms is that ripping cuts are all cuts along the grain but not all rip cuts are resawing.
Resawing, as the term is used today, refers only to cutting a board across its thickness, i.e. sawing a thick board into two (or more) thinner boards. You are literally re-sawing the board from its original sawn thickness.
A standard rip cut performed on the same starting board would be reducing its width.
For instance, if I were to saw a 4x4 into two 2x4s, is that operation a rip or a resaw?
It's both, but wouldn't normally be referred to as a resawing operation.
I don't think this is because a 4x4 isn't generally referred to as a board (although that distinction is largely arbitrary), but if you sawed it instead into three or four or five boards, that would then be resawing certainly even if it wouldn't commonly be thought of or described that way — lots of idiosyncratic or irregular use of terminology in woodworking, as well as regional and dialectical differences.
It would seem to be more reasonable to label the cut according to it's orientation relative to the grain like we do with the crosscut.
No, because the orientation of the grain, as I think you're referring to, isn't relevant. Resawing is a type of rip cut as already stated, so in one way the cut is always along the grain but the angle of the cut as it relates to the grain in the wood the other way (more radial than tangential, more tangential than radial) is not relevant to the type of operation, thinning the board is the only criterion that defines resawing.
Bonus question: Is there research that discusses the differences in these two cutting processes?
I'm giggling inside at this, we do love to over-analyse things. Anyway not that I'm aware of. Why would there need to be? We can call resawing anything we want for all the difference in makes in what the operation is, or how it's done.
I bet in other languages resawing wouldn't be a simple translation of re- saw, it could be a specialist woodworking word stemming from the historical name for the cut with no exact parallel in English (there are a few examples of this in French, German and Swedish).
But regardless of the word(s) used in all cases it will simply refer to a type of rip cut performed to cut a thicker board into thinner boards.