This is actually an interesting question of language. Even the very name of the war itself often changes depending both on region and the decade in which the speaker/writer is discussing it.
The regional terms (North/South) were at least nominally accurate at the time, though the map to modern Americans looks more like "The rest of the United States/Southeast". The rhetorical term (Rebel/Yankee) are perfectly acceptable in context of the period; the seceding states were, after all, in rebellion - and had little problem accepting that - and by the nineteenth century, the term "Yankee" was a general term for any American from a non-slaveholding state, despite originally referring only to New Englanders. The political term (Union/Confederate) is just as accurate as "United States" and "Confederate States" - Union being a shorthand for the former.
It is worth noting, of course, that "Confederate States" and variations thereof was a self-bestowed title; legally, the people of the various states of the Confederacy were citizens of the United States who resided within states in rebellion. Ultimately, this is merely an issue of semantics, and unless one is intentionally trying to be inflammatory, it doesn't really matter what you call them.