Of course it matters. That's not the question. The question needs to be understood as, what did they mean?. My contention is that they meant no more and no less that citizenship by birth. Otherwise they would have needed to define the distinction, and they did not.
Where is there any commentary by a Framer, or anyone who knew them, that says that that is all they meant, as opposed, say, to Jay’s concern in his famous letter to Washington, about dual allegiance?