Oh don't be stupid. The phrase "or out of the limits of the United States" was in both acts. This would also include areas "beyond the seas", so "beyond the seas was redundant. Citizen at birth and Natural Born citizen are also redundant.
This is not true. Natural Born Citizens existed after July 4, 1776 without any resort to statute law. It is obvious that their existence is not dependent upon statute law.
Therefore, someone who's citizenship *is* dependent upon (subsequent to 1776) statue law, cannot be the Natural Born citizens which the founders spoke of in 1787.