[jamese777]

Correct. As previously stated, the Constitution mentions two types of citizens, and only two.

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And courts have ruled that “citizen at birth” and “natural born citizen” are synonomous terms. The other category is “naturalized” citizen.

[rxsid]

"And courts have ruled that “citizen at birth” and “natural born citizen” are synonomous terms. "

What court(s) have made the two synonymous, especially with regards to the qualifications for POTUS?

[Seizethecarp]

“And courts have ruled that “citizen at birth” and “natural born citizen” are synonomous terms.”

Wrong.

In the Minor case, SCOTUS identified two types of citizen at birth on US soil as of the date of their ruling:

1. Children of US citizen fathers about which there “is no doubt” that they are NBC.

2. Children of foreign citizen fathers about which there “is doubt” that they are NBC.

These are two distinct classes of “citizen at birth” who are not in the naturalized category. The doubt in the Minor case was not resolved in Wong because SCOTUS could not “reach” that determination in the case before it. And that doubt established in Minor remains unresolved, as far as I can see, because no subsequent, on point case has explicitly reached the NBC issue.

So there “is doubt” about Obama’s NBC status per SCOTUS in Minor.