The Constitution requires that you be a natural born citizen in order to be eligible to become president of the United States. Some people argue that it is sufficient to be a citizen at birth. But if you look at title 8 section 1401 you will find all kinds of ways in which you can be a citizen at birth. One of them is even if you are found as a baby in the woods and you have to wait until you're 21 and as long as no one has proved that you were not born in the United States you can be considered to be a citizen at birth. That doesn't sound like the kind of thing that anyone would consider to be a "Natural Born" citizen.
So I think the only reasonable interpretation of natural born is part (a) of section 1401. Namely that you are born in the territory of United States.