My distinction is simple: as I stated in my "assumption," they didn't have a JFK airport or Ellis Island in the 1780s with ships coming in every day by the dozens or hundreds. It would be weeks or months before a ship arrived.
In those times, if you were born here you born to natives who were already here.
I'm saying that in the language of the time, it was assumed that native or natural born in America were born to the already established citizens of the country.
I read in the Commentaries of Blackstone that in England it was assumed that a child of aliens born in England was considered to be a natural-born subject, but in France the child of an alien born if France is still an alien. The assumptions were different in Europe because the countries were very close and many shared borders where cross-border travel was common.
Cross-border travel in America was not so easy because you had to cross the Atlantic in a 3-mast ship, which was an expensive endeavor.
An assumption? Yes, but a reasonable one to make.
I don’t really see the difference between a pregnant woman who boards a ship and comes to America. Sure, a few days is not the same as a month shipboard time. The concept is the same.
Or those who fully intended to become citizens. People didn't come here on a whim. They came here to settle.