Natural born citizenship is not a type of citizenship. It is ONLY an eligibility requirement to be President of the United States. Its sole appearance in our legal system is in Article II, Section 1, of the United States Constitution.
The types of citizenship recognized by legal statute are: native born citizenship (jus solis); derived citizenship from parent(s)(jus sanguinis); or, naturalized citizenship. See: USCIS for further information.
The 14th Amendment has no impact on Article II’s eligibility requirement.
The Supreme Court disagrees with you. In Minor v. Happersett, Justice Waite clearly referred to natural born citizenship as a class of citizenship when he defined it.
At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that 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, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their [p168] parents. As to this class there have been doubts, but never as to the first.
I bolded where Waite talks about these two classes of citizenship. The context is important here because Waite offered this definition to explain that women who are natural born citizens do not need the 14th amendment to give them citizenship.
There is no doubt that women may be citizens. They are persons, and by the fourteenth amendment "all persons born or naturalized in the United States and subject to the jurisdiction thereof" are expressly declared to be "citizens of the United States and of the State wherein they reside." But, in our opinion, it did not need this amendment to give them that position. Before its adoption the Constitution of the United States did not in terms prescribe who should be citizens of the United States or of the several States, yet there were necessarily such citizens without such provision.
Waite reiterates this point later in the decision specifically in relation to Viriginina Minor, who had claimed a right to vote as a 14th amendment citizen. Waite rejected her claim because she was a natural born citizen.
The fourteenth amendment did not affect the citizenship of women any more than it did of men. In this particular, therefore, the rights of Mrs. Minor do not depend upon the amendment. She has always been a citizen from her birth, and entitled to all the privileges and immunities of citizenship. The amendment prohibited the State, of which she is a citizen, from abridging any of her privileges and immunities as a citizen of the United States; but it did not confer citizenship on her.
The Wong Kim Ark decisions cites Waite's definition of natural born citizen and affirms that Minor was found to be a citizen on the basis of BOTH jus soli and jus sanguinis criteria.
Minor v. Happersett (1874), 21 Wall. 162, 166-168. The decision in that case was that a woman born of citizen parents within the United States was a citizen of the United States ...
We get from these two decisions that Natural Born Citizenship is defined outside of the Constitution and Statutory Law. Citizenship by birth via the 14th amendment is a separate Constitutionally defined type of citizenship that excludes natural born citizens, but that one's parents must have permanent domicil and residence in order to meet the requirement of being subject to the jurisdiction. There are other types of statutory citizenship by birth, but these are not to be confused with natural born citizenship.