“What is the difference between a mere “born citizen” (the Founders considered this phrase, but rejected it) and the more restrictive natural born Citizen...”
First, we have no idea what was considered on this clause of the Constitution. There are no records of any debate on this clause. However, Natural Born Subject was a well known legal term used by the Founders often during their colony days, and it simply meant born as a subject.
By restricting Presidents to NBC, they rejected naturalized citizens from the presidency. There were only two categories: Natural born or naturalized. Still are only two.