IMO the distinction is right there in the wording of the Amendment. Foreign citizens are ultimately subject to the jurisdiction of their native country. Thus the ability of a foreign nation to intervene with appeals on behalf of their citizens who run afoul of the law in the U.S. It is self-evident, or should be, that the newly born offspring of a foreign citizen is also subject to the jurisdiction of their parent's native country.
Lacking a court ruling to affirm that interpretation it can certainly be clarified with additional legislation but the distinction already exists in the 14th Amendment and the Executive Branch could simply assert that it is the policy, in accord with the 14th A., that children born here of foreign citizens are not U.S. citizens.
No, foreign citizens in our country are subject to US jurisdicition, just like any citizen. They are required to obey our laws and can be punished for any violatoins just like us. Even if they are here illegally.