It is interesting that in Article I Section 2 of the Constitution speaking to eligibility of Representatives and Section 3 speaking to eligibility of Senators that the Founders stipulated very simply ‘Citizen’ only. In contrast in Article II Section I the Founders explicitly declared that future persons to be eligible for President must be a ‘natural born citizen ‘. I don’t believe these educated,versed in law Founders would have been haphazzard when it came to embedding different terminology as to eligibility. There were deliberate intentions for stipulating differences as to citizen.
They were saying that citizens that were not natural born (i.e. naturalized) were perfectly able to serve as Senators and Representatives, but not the Presidency.