Becasue there is no difference between being a citizen, either at birth or naturalized, *except* for eligibility to the office of President. There is NO LAW, passed by Congress, defining Natural Born Citizen. If you have a referance to one, post the link to it.
I can't prove the negative that there is no such law, but logically there cannot be, for the Congress cannot define the meaning of a Constitutional term, for purposes of the Constitution. Otherwise they could change the meaning of Constitutional provisions without bothering with the amendment process. If they can do that, we don't have a written Constitution at all, just something to be reinterpreted as Congress desires. The could define "arms" to mean "swords and knives..well maybe not knives" for example. And then proceed to infringe upon the right of the people to keep and bear arms
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Oh wait they do that anyway, but they do it by ignoring the second amendment, not redefining it's terms.
Or if by "the law" you mean the case law as well as the statute law, then the same is still true. The Courts have hinted at definitions in dicta, but since they have not heard a case on eligibility to the office of President (on the merits), they haven't actually defined it.
You are right, Congress has passed no law creating a difference between “citizen by birth” and “natural born citizen”. So why do you keep insisting that they are different things?