If a kid is born in Kansas in 1888 to parents born in Kansas, what's it's citizenship?
If a kid is born in Kansas in 1888 to a mother born in Mexico and a father born in Kansas, what's it's citizenship?
In the 2nd case, you'd have to look up the law at the time of birth because the kid would not always have been a US citizen. It would be a US citizen at this point in time because a change in immigration law naturalized it.
The first case is natural born because you don't need a law to determine it. A child of natives is natural born.
Citizen at birth does not equal a natural born citizen.