In some world only the “natural born” contingent inhabit, citizens mentioned in the 14th amendment are different than those mentioned in the original constitution. Pity for them, there is no explanation of that in the law, nor has SCOTUS agreed with them. You have nothing where SCOTUS specifies “14th amendment citizens have fewer privileges than ‘other’ citizens,” or that 14th amendment citizens are distinguished legally from others. Unless you butcher quotes, of course.
The Constitution uses a term that the Supreme Court said was not defined by the 14th amendment, so it is what it is. The intent of the founders was to provide a strong check against the admission of any foreigner as the commander in chief. Such a check is rendered moot if the 14th amendment or statutory legislation provides the only criteria for establishing the citizenship of a presidential candidate. The Supreme Court said, “Yes, Viriginia, there is a difference” and explained why with a doubt-free definition.