Your error is your mischaracterizing of the quoated statements. See Sir Edward Coke Calvin’s Case and the difference between datus and natus. Your quotations clearly recognize the differences in their usage of such terms a “deemed” “considered” and so forth to indicate the person is not what they are deemed but will be treated as if they were, meaning they are artificially made so by the manmade law instead of by nature.
I made no error. The point, which you have missed entirely, is that NBC & NBS were being used interchangeably by one of the legislatures that ratified the US Constitution. Thus NBC = NBS, and NBS had an established legal meaning.
Natural born citizen was a legal phrase. It was not something made up for use in the Constitution. It was in use, by legislatures, several years prior to the writing of the Constitution.