I am curious what your thoughts are about why the founders made the distinction between "natural born Citizen" and “citizen” in the Constitution.
No Person shall be a Representative who shall not have attained to the Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.
No Person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.
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; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
It's simple: they wanted to distinguish between born citizens and immigrants. The latter are people who were not born citizens but became citizens later on through naturalization. Examples include Kissinger and Schwarzenegger and, as the article mentions, in 1786 threatened to include Prince Henry of Prussia and George III's little brother Frederick, Bishop of Osnaburgh.
The Founders decided it was OK for immigrants to serve in the House and Senate, but that the presidency should be reserved for natural born citizens, in order to exclude the likes of Prince Henry and Prince Frederick. There would be no Emperor Maximilian I of the United States.