That would make sense. While all are citizens, not all are natural born citizens.
The natural born form is better understood as an exclusive, pure kind of thing rather than such a loose standard or there would be no point of making any citizenship distinction or reason to mention "natural born citizen" at all.
Moreover, both the 1790 and the 1795 definitions highlight the citizenship status of the father at time of the child's birth and a foreign father cancels the American at birth citizenship thing altogether.
So much for anchor baby citizenship, too.
No. I am saying there was and is only two types of citizens:
Naturalized through a legal process
Natural born