That was a statement in a debate, not law. If that were law because it was said in Congress, every idiotic thing Cynthia McKinney said in Congress would be law, too.
Natural born citizen is solely, per the U.S.Constitution, an eligibility requirement to be President. It is Natural Law and does not need a statute for its definition.
Why? Because a child born in a nation of citizen parents doesn’t need no stinking law to be recognized as a natural born citizen.
The statutory types of citizenship can be found here:
USCIS - Citizenship