There are three kinds of citizen.
Natural born, native, and naturalized.
The culture war on America has been so successful few are left with the cultural knowledge to refute your false claims.
Native and natural born are interchangeable.
As the President is required to be a native citizen of the United States . Natives are all persons born within the jurisdiction and allegiance of the United States.
James Kent, COMMENTARIES ON AMERICAN LAW (1826)
That provision in the constitution which requires that the president shall be a native-born citizen (unless he were a citizen of the United States when the constitution was adopted) is a happy means of security against foreign influence...
St. George Tucker, BLACKSTONES COMMENTARIES (1803)
“Suppose a person should be elected President who was native born, but of alien parents, could there be any reasonable doubt that he was eligible under the constitution? I think not.”
Lynch, 1844. Notice it assumes native born can have two citizen parents.
“”Young Steinkauler is a native-born American citizen. There is no law of the United States under which his father or any other person can deprive him of his birthright. He can return to America at the age of twenty-one, and in due time, if the people elect, he can become President of the United States...” - from Perkins v Elg
“But the Secretary of State, according to the allegation of the bill of complaint, had refused to issue a passport to Miss Elg “solely on the ground that she had lost her native born American citizenship.” The court below...declared Miss Elg “to be a natural born citizen of the United States,” and we think that the decree should include the Secretary of State as well as the other defendants.” - Perkins v Elg
“Before our Revolution, all free persons born within the dominions of the King of Great Britain, whatever their color or complexion, were native-born British subjects; those born out of his allegiance were aliens. . . . Upon the Revolution, no other change took place in the law of North Carolina than was consequent upon the transition from a colony dependent on an European King to a free and sovereign State;”
State v. Manuel, 4 Dev. & Bat. 20, 24-26 (1838)