The Constitution makes it clear that native-born means that you're a citizen at birth. There's nothing in the Constitution that creates a separate class of citizens who are born as U.S. citizens but not actually natural-born citizens.
Do some research. Read Benjamin Franklins letters written during the writing of the constitution where he discusses researching Latrell’s writings on natural born( although that is not the exact term Ben used)
Then read John Jay’s letter to George Washington
It is all right there
The 14th Amendment to the Constitution did that for those "subject to the jurisdiction of the states" and it only made one a "citizen" -- not a "natural born citizen".
There's nothing in the Constitution that creates a separate class of citizens who are born as U.S. citizens but not actually natural-born citizens.
Except for Article II of that Constitution.
Why did they use the term Natural Born Citizen instead of Native Born Citizen when they set the requirements for President?
The Constitution does not use the words "native born". Modern usuage of that term means "born in the country", but various earlier writers including Vattel (in translation) use the terms "native born" and "natural born" more or less interchangeably. (Vattel of course used "Les Naturels, ou Indigenes", since he was writting in French") So did the Supreme Court in Minor v. Happersett, where they wrote: "all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens"
Clealy they required more than the 14th amendment's "Born in the United States", which is what we today call "native born".