Wrong way to look at it.
Natural Born Citizen has always meant Citizen at Birth.
However, when Common Law controlled this issue, both terms still meant the same thing.
The Founders meant that you had to be a Citizen at Birth, and at the time they wrote and ratified those words, they also gave Congress the power to define Citizenship clearly.
They gave Congress the power to define Naturalization rules, not citizenship, unless you can point to a Constitutional clause stating otherwise.