The common law of England is not the common law of these States. George Mason
What Natural-Born Citizen Could Not Mean
Could a natural-born citizen simply mean citizenship due to place of birth?
Unlikely because we know one can be native born and yet not a native born citizen of this country prior to the year 1866. There were even disputes whether anyone born within the District of Columbia or in the territories were born citizens of the United States (they were referred to as inhabitants instead.) National Government could make no territorial allegiance demands within the several States because as Madison explained it, the powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State.
Fourteenth Amendment
Whatever might had been the correct understanding of natural-born citizen prior to 1866, the adoption of the Fourteenth Amendment certainly changes the view because for the first time we have a written national rule declaring who are citizens through birth or naturalization. Who may be born citizens is conditional upon being born subject to the jurisdiction of the United States - a condition not required under the common law. The legislative definition of subject to the jurisdiction thereof was defined as Not owing allegiance to anybody else.
This national rule prevents us from interpreting natural-born citizen under common law rules because it eliminates the possibility of a child being born with more than one allegiance.
Natural-Born Citizen Defined
One universal point most all early publicists agreed on was natural-born citizen must mean one who is a citizen by no act of law. If a person owes their citizenship to some act of law (naturalization for example), they cannot be considered a natural-born citizen. This leads us to defining natural-born citizen under the laws of nature - laws the founders recognized and embraced.
Under the laws of nature, every child born requires no act of law to establish the fact the child inherits through nature his/her fathers citizenship as well as his name (or even his property) through birth. This law of nature is also recognized by law of nations. Sen. Howard said the citizenship clause under the Fourteenth Amendment was by virtue of natural law and national law.
Your post is about what the law should be, not what it is.
The Supremes have never ruled precisely on the "natural-born" issue, but it really isn't difficult to examine the rulings they have made and deduce how they likely would rule. Which would be that natural-born is the same as native-born, leaving us with two categories of citizenship, not three.