In the Ark decision, Justice Gray did state that the U.S. recognized two classes of citizen - citizen at birth and naturalized citizen. Obviously the intent is that citizen at birth and natural born citizen are synonymous.
This has always been my understanding as well, and what I have maintained consistently. So far there has been much fussin and hollerin, but no actual rebuttal to this point.
There are two types of citizens in the USA, naturalized and natural born. Natural born citizen means that by the natural act of being born, you had citizenship conferred upon you, and are thus a “natural born citizen” rather than a “naturalized” citizen who had to go through a legal process to attain citizenship.