I would argue that it is a "term of art" specifically know to the founders by their reading and familiarity with the writings of Grotius, Pufendorf and Vattel, who's collective works and Vattel's specifically, are referred to as the Laws of Nations.
It was simply a term used to describe someone that wa sa citizen by birth, nothing complex or complicated about it.
Your response is an excellent illustration of why birthers have fallen flat on their face in Congress, every state legislature and court (federal or state)in their feeble quest to change the law. Maybe if birthers respected the rule of law in our society, they may be a little bit more successful.