In the Happersett case the Court addressed the issue of subject vs. citizen. They don't seem to place enormous importance on which word is used.
For convenience it has been found necessary to give a name to this membership. The object is to designate by a title the person and the relation he bears to the nation. For this purpose the words "subject," "inhabitant," and "citizen" have been used, and the choice between them is sometimes made to depend upon the form of the government. Citizen is now more commonly employed, however, and as it has been considered better suited to the description of one living under a republican government, it was adopted by nearly all of the States upon their separation from Great Britain, and was afterwards adopted in the Articles of Confederation and in the Constitution of the United States. When used in this sense it is understood as conveying the idea of membership of a nation, and nothing more.
IOW, it's pretty clear the Court considered the terms "subject" and "citizen" more or less synonymous. They certainly don't seem to draw great conclusions from which word is used.
The entire legal history of the US shows that, with exception of LA, common law has been the standard except where overridden by statute or judicial decision. Changes are made in terminology as appropriate for a republic vs. a monarchy. Citizen rather than subject, state rather than crown, etc. But the principles were transferred over with little change. This was even more true in the early years of the nation.
Well that's an interesting way to look at it. What you've ignored is that the Court addressed the specific definition of natural born citizen: all children born in the country of parents who were its citizens. The Wong Kim Ark decision quoted and affirmed this definition more than 20 years later. It only relied on British common law to give teeth to the 14th amendment, but clearly distinguished its type of citizenship from natural born citizenship.