This is what the Constitution of the United States, Article II, Section 1, Clause 5 says:
“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.?
That is all the Constitution has to say regarding this situation.
So a "Citizen of the United States, at the time of the Adoption of this Constitution" is not the same as a "natural born Citizen".
And to be elected to Congress one must be a "citizen" as opposed to a "natural born Citizen" to be elected President.
Why do you suppose the different terms were used. Were the founders merely sloppy?