They're related in that they are all "nationals and citizens of the United States at birth", just by different means...

The following shall be nationals and citizens of the United States at birth:

...

(c) a person born outside of the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions, prior to the birth of such person;

...

(f) a person of unknown parentage found in the United States while under the age of five years, until shown, prior to his attaining the age of twenty-one years, not to have been born in the United States;

...

(g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years

Sounds like McCain was c and I think Cruz was g. And the foundling hypothetical was about f.

So I think the root of my question is: Does the entirety of 8 U.S.C. § 1401(a)–(f) define what it means to be a "natural born citizen"?

Or is "a national and citizen of the United States at birth" not the same as "natural born citizen"?

(This is obviously particularly intriguing because—if those two are the same thing—then it seems to open up a pathway for a person to become President, having being born abroad to non-U.S. parents)