"Natural citizen" is not a legal term. (Did you mean to say "natural-born citizen"?)
Nor does "natural law" (which is a broader term corresponding to unchanging moral principles intrinsic to human nature, and is thus inherently separate from civil law per se) have anything to do with questions of what it means to be a citizen of a country, or what it means to be subject to the jurisdiction of a country (which are all questions of positive law, quite separate from the natural law).
That the legal system has not deigned to embrace it signifies nothing to me. It is a plain and simple description that gets the point across, and indeed, is far clearer in purpose from having left off the "born" part of it. All people are "born" so it is just redundant.
Nor does "natural law" (which is a broader term corresponding to unchanging moral principles intrinsic to human nature, and is thus inherently separate from civil law per se) have anything to do with questions of what it means to be a citizen of a country,
To the contrary. Without the "natural law" foundation for our independence, we are "subjects", not "citizens."
"Citizen" does in no way derive from English common law. The understood meaning of the word "Citizen" in 1770s England was "Dweller in a City."
Their proper word for someone owing allegiance to a nation was "Subject."
The word "Citizen", in our understanding of the term, does not come from England.