Yes, it is obvious that "natural born citizen" is narrower than "citizen." "Natural born citizen" excludes "naturalized citizens," who are born as foreigners. The framers wanted to prevent the possibility of a foreigner emigrating to the U.S., becoming a citizen, and becoming President.
You are ignorant of the history of the United States to the point that you are lying to yourself and others when you call yourself a Conservative.
To be a Conservative you must first know what it is you are conserving. You have no idea, and I’d suggest that you do yourself a really big favor and learn.