Before the 14th Amendment and the SCOTUS opinion in US v. Wong Kim Ark, natural born and native born were one and the same. The courts then had to differentiate the two terms for someone born in country but not a natural born citizen. The law of England that makes "natural born subjects" out of children born of foreigners is a naturalization law, and therefore, those children are not not natural born citizens. The same man-made law that Justice Gray used as justification in his 1898 to make Wong Ark a citizen when he legislated from the bench.
The word "natural" in the phrase 'natural born subject' is a misnomer.
Since Great Britain and its empire is under a monarchy, it was understandable to use the word "natural" as the monarchy wanted to ensure obedience from even the foreigners in their empire.