[Lurking Libertarian]

Law of Nations is twice mentioned in the U.S.Constitution,

Yes, to mean what we call today "international law." It's not a citation or endorsement of Vattel's book.

English Common Law never

Try reading the Seventh Amendment, which mentions it twice.

[plenipotentiary]

What’s the difference betwen a US Citizen, a Naturalised Citizen, and a Natural Born Citizen? They have to be different because they are all used as separate terms in US Statute Law, and in the Constitution.