And that is laid out in the Constitution where exactly?
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.That isn't exactly the statement made by your opponent in argument, who said "Statutory citizenship = citizen. Common law citizen = natural born citizen." But Article IV sets out who is a constitutional citizen.
One can be pedantic and say that natural born citizen isn't defined in the constitution, but citizen (of the US) is defined, and by implication, a person who is born a citizen of one of the several states is naturally born a citizen of the US. There wold have been 13 different rules for citizenship at the time of founding.
The 14th amendment makes the definition of US citizen more uniform across the US, making everyone born in the US and subject to the jurisdiction a citizen. This sweeps in the children of slaves and assorted others. It also makes naturalized citizens into citizens, but that's a bit of a tautology.