[edge919]

A natural-born citizen is a citizen from time of birth. Those are synonymous terms. Any definition of a citizen from time of birth is therefore describing a ‘natural-born citizen’.

This is wrong. There are several types of statutory citizens at birth that clearly aren't natural born citizens. Natural born citizenship is such that you are born with direct ties to the country where you were born. The presidential eligibility requirement is to exclude all persons born with ties to foreign countries.

[WOSG]

“There are several types of statutory citizens at birth that clearly aren’t natural born citizens.”

If you are a citizen at birth in the US, you will be eligible to be President. Unless you have a court statement or ruling backing up your view, that’s just your own supposition/definition, contrary to common understanding of the term.