No. The 14th didn't "change" anything other than re-enforce and acknowledged that one could become a United States "citizen" by either being "born" or "naturalized" in the United States.
From the Congressional Research Service: (Page 2)
"There is no provision in the Constitution and no controlling American case law to support a contention that the citizenship of one’s parents governs the eligibility of a native born U.S. citizen to be President."
That's correct. It acknowledged that one could become a citizen by being "born" in the U.S. or "Naturalized" by the U.S. We are in agreement. It says nothing about folks who are "Natural Born Citizens". You can be born in this country..... but yet not be a "Natural Born Citizen".....but still be considered a citizen. You just cannot run for the presidency.
The Constitution no where defines the term "Natural Born Citizen" so we must look elsewhere for a definition. Because it no where defines the term.... the 14th Amendment does not affect it. The 14th Amendment addresses the problem of freed slaves and their citizenship distinctions. Prior to the ratification of the 14th Amendment each individual state had the right to determine who and what were citizens within their own borders. States varied in their requirements but usually free "White" children born within that particular state (except children of foreign ambassadors and nomads) were considered citizens of that state.
The 14th Amendment defined a particular group of people who were born or naturalized in the U.S. and were subject to the jurisdiction thereof at the time of their birth. The 14th Amendment required each state to recognize the citizenship of these folks. The Amendment does not say anything about the meaning of "Natural Born Citizens". The notion that it implies folks born on U.S. soil are "Natural Born Citizens" is not consistent with the clause which states: "Subject to the jurisdiction thereof".
Now.....did the Supreme Court of the land know the meaning behind the words "Natural Born Citizen". Of course they did! In 1856 the infamous Dred Scott decision was rendered by the U.S. Supreme Court. Chief Justice Taney rendered the opinion of the Court which was echoed by Justice Daniel in his own opinion which included these words:
"By this same writer it is also said: 'The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority; they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As society cannot perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their parents, and succeed to all their rights.' Again: 'I say, to be of the country, it is necessary to be born of a person who is a citizen; for if he be born there of a foreigner, it will be only the place of his birth, and not his country. The inhabitants, as distinguished from citizens, are foreigners who are permitted to settle and stay in the country.' (Vattel, Book 1, cap. 19, p. 101.)
From the views here expressed, and they seem to be unexceptionable, it must follow, that with the slave, with one devoid of rights or capacities, civil or political, there could be no pact; that one thus situated could be no party to, or actor in, the association of those possessing free will, power, discretion. He could form no part of the design, no constituent ingredient or portion of a society based upon common, that is, upon equal interests and powers. He could not at the same time be the sovereign and the slave."
Definition of Unexceptionable: incapable of being criticized: good enough to provide no reason for criticism or objection
There are.....and always have been three classifications of Citizens. "Natural Born Citizen"....born to Citizen Parents. "Citizen"....born in U.S. to Alien Parents. And "Naturalized Citizens"....born abroad and fulfilled the Constitutional requirements for Citizenship.
The reason these things are not readily understood by many 21st century Americans (perhaps by you as well) is the simple fact that the Constitution has not been taught in our public Schools for perhaps 50 years or so. When I was in grade school we were taught (circa 1950/55) what "Natural Born Citizens" were and we indeed had one young girl in our class whose parents had been displaced persons from Eastern Europe who were immigrant Aliens in this country when their daughter had been born in 1942. I can remember our teacher telling us that, "Yes....she is a citizen..... but since mom and dad were not yet citizens she was not considered Natural Born".
I since have not heard of her attempting a run for the presidency.