Since the adoption of the 14th Amendment there are only two types of American citizens: born citizens (same as natural born) and naturalized citizens. Born citizens can be president and naturalized citizens can’t.
Wong Kim Ark could not be a naturalized citizen due to the Chinese Exclusion Act in force at that time.
The US government’s attorneys were certin that they were dealing with a natural born citizen question. In their respondent’s brief for the Supreme Court, they wrote: “Are Chinese children born in this country to share with the descendants of the patriots of the American Revolution the exalted qualification of being eligible to the Presidency of the nation, conferred by the Constitution in recognition of the importance and dignity of citizenship by birth? If so, then verily there has been a most degenerate departure from the patriotic ideals of our forefathers; and surely in that case American citizenship is not worth having.”
http://www.scribd.com/doc/23965360/Wong-Kim-Ark-US-v-169-US-649-1898-Appellants-Brief-USA. (See page 34 of the original document)
That was also true prior to the 14th Amendment.
The 14th Amendment did not change this, WKA did.
See Post 297