You’re either a “Natural” or “Naturalized” citizen. One is ‘by birth’ and the other ‘by paperwork’.
Natural born isn't about the person's birth location. Natural born is about the location of both parent's birth.
The founders had a serious concern about divided allegiances if either of the president's parents were natives of a different country.
The founders alleviated their concerns by adding this restriction on presidential candidates but not on congressional candidates.
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;
The Constitution distinguishes between citizens and natural born citizens, not between naturalized citizens and natural born citizens.