a) Based on a French text on Natural Law actually present at the Constitutional Convention in 1789: A "natural born" subject of a sovereign (or citizen of a republic) is one where i) both parents are subjects/citizens at the time of birth; AND ii) the parents are married (bastards are not "natural born" subjects, most likely because parentage is in doubt).
b) As laid out on National Review: a "natural born" citizen is anyone who is a citizen without having to go through the legal process of naturalization. The NR author argues this was understood by the Founders when they gave control of naturalization legislation to the Congress.
Personally, I'm inclined to (a), simply because if Congress had plenary authority over naturalization, it could simply declare in law that all residents of the US (or the world, for that matter) do not need naturalization.
But I tend to think that (b) is really what everyone means by "natural born." The only complication is those born in the US to parents who are not citizens.
THIS is where they try to trip you up. Automatic naturalization requires no *process*, but that doesn't mean that child is a natural born citizen.