You did not answer the question posed to you. I did not introduce a fourth category of citizenship, but you must for your theory to hold water.
What is the reason for the distinction between “citizen” as a requirement for Senator and Representative and “natural born” citizen for President?
Of the three categories of citizen mentioned in the Constitution, any of the three may be a Senator. A non citizen cannot be a Senator. Only a natural born citizen or a citizen at the time of the adoption can be President. A naturalized citizen or a non citizen cannot be President.