You have still yet to cite anything suggesting that there has ever been a third "type" of citizen. You have not read what I have cited. Read what BP2 posted, then read Tucker said -- and Bingham in the article which starts this thread.
They are both utterly clear: 1. born in the nation and, 2. born of an American citizen father.
Except that all of those sources are, in context, discussing the notion of citizenship generally. To those writers, a person born of non-citizen parents was not a citizen at all. They were drawing a distinction between citizen and non-citizen, not between "natural born citizens" and "citizens simply born in the country." The writers you quoted
still do not support the proposition that there is some sort of third type of citizenship - it's still simply "citizen" v. "non-citizen."
To the writers you quote, an individual who met your qualification (1), but not (2) would not be a citizen. This is a concept of citizenship that has been rejected in this country - via statute, case-law, and understanding of the Fourteenth amendment - for well over 100 years.