I'm not conflating anything. If the only difference between two people, ag and sex being the same for instance, is that one is a citizen (or permanent resident) and the other is a visior on a student visa, then the fact that they are differently treated, in something like the draft which is the government exercising it's jurisdiction over it's citizens, then it's clear that the visitor is not subject to the full jurisdiction. IIRC, We went to war with the British, in part because they were trying to "Draft" (Impress was the word used in those days) our merchant sailors into their Navy. (1812)
However, I do believe that if one parent is an American citizen, and the other is a permanent legal resident, then you are a "natural born" citizen if you are born on U.S. soil. I fall into that particular category.