As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it.
The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country."
Yep I read it quite clearly as well as the heading of the section: Citizens & Natives.
That clearly indicates that they are two separate designations: Citizens and Natives(aka Native Born Citizens).
The section I appended earlier deals with Natives as distinct from Citizens the sections that follow deal with citizens: by naturalization, citizenship of those born in a foreign country, at sea, in armies of the state and of inhabitants of a country as opposed to citizens.
Seems pretty straight forward & businesslike to me, laid out in an orderly fashion with definitions and situation analysis. One class of natural born and the many ways a person could be considered a citizen. Letters between the Founders at the time of the writing indicate they concurred.