I agree that natural born and naturalized are two distinct things. The only argument concerning natural born is over who is and isn't such as in Obama's case. Some were trying to make the argument over whether or not he was a natural born citizen making him subject to disqualification under the 'natural born citizen" clause.I consider the "natural born citizen" clause to be largely moot at this point. Obviously, naturalized citizens are still denied eligibility under this clause. But the original intent had broader meaning and impact, in a newly born country. Once all citizens were "natural born" by virtue of having citizenship through birth in the USA, the import and ambiguity of the "natural born citizen" clause was considerably mooted.
It's simple: if your citizenship in the USA is by virtue of your birth, you meet the "natural born citizen" criterion. If you are a naturalized citizen, you do not.