Native born and Natural born are the same in the Law of Nations, the reference used for the Constitution.
A beg to differ. Not according to two Supreme Court decisions, 1939 Perkins v. ELG and 1898, Wong Kim Ark v. U.S. which makes it clear who is and who is not a natural born citizen.
http://www.freerepublic.com/focus/news/2151845/posts?page=226#226