They had to make that distinction because at the time of ratification, no one would have qualified as a natural born citizen of sufficient age to be president, so they may an “initial condition” exception.
Yes, as you said, there IS a distinction between “natural born citizen” and “US Citizen”.
Now, if concern troll wants to say that we should ignore this qualification, go for it. State that the Constitution’s requirements and restrictions shouldn’t be adhered to today.
The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Minor v. Happersett, 88 U.S. 162, 168.
Emphasis added
Attempts to redefine or amend Article II natural born Citizen Clause of the U.S. Constitution
You have to know what the definition is before you can change it.