Logically there must at least be the possibility of a difference. Congress defines "citizen at birth". But Congress cannot redefine any terms of the Constitution. (Except by amendment of course, but that they cannot do alone). Thus Congress could, and has many times, changed the requirements for "Citizen at Birth". They have only amended the Constitution once to define who is a citizen, and even then did not actually use the term "natural born citizen". With that exception, "Natural Born Citizen" must mean now what it meant when the Constitution was written and ratified. It is after all a contract, and except under conditions specified in that contract, the meanings of it's terms cannot be changed by either/any party to that contract.
Otherwise congress could declare that "right of the people" actually meant "power of the states".
Why?
But Congress cannot redefine any terms of the Constitution. (Except by amendment of course, but that they cannot do alone).
But the term is not defined by the Constitution in the first place. And the Constitution gives Congress the power to create uniform laws for naturalization. How can you define who can be naturalized and how if you do not first define who doesn't need to be naturalized? In other words who are citizens at birth? And that is what Congress has done, and what the Supreme Court has upheld.
Otherwise congress could declare that "right of the people" actually meant "power of the states".
There are those who would say they already have.