What matters is that natural born subject was a very well known and very commonly used legal phrase in the colonies, and it was used interchangeably with natural born citizen for some years after the Constitution.
And that legal meaning included the children of aliens, unless the aliens were ambassadors or in a foreign army.
NBC was NOT an appeal to European ‘natural law’, but to a term used regularly by every legislature that ratified the Constitution. They didn’t need to define it because it was already a well known and defined term.
A naturalized subject was considered a natural born subject for all intents and purposes. A naturalized citizen is not considered a natural born citizen.
According to English common law, a natural born subject was required to be a Christian. A natural born citizen could be any religion...or none.
There are far too many differences between to two to try and force them to be equal.
And yet when Chief Justice Marshall wishes to cite the law on Citizenship he turns to Vattel, not Blackstone. So does Justice Washington.
WOW! Where is your head kept?