Actually, they don’t have to mean something different. It’s not uncommon in laws and regulations to use differing terms interchangeably, particularly when the usages occur over time. You can even find laws and regulations which subsequently specify that certain historical terms are equivalent.
So the framers invented “Natural Born Citizen” for the Presidential qualification, even though in your estimation it has the same meaning as “Citizen”?
I don’t think you really believe that do you?