Do not understand it. It makes no logical sense. Never has, never will.
Mexicans are people who live in Mexico. They have Mexican passports. The same way the British have United Kingdom passports. The general classification for people from foreign countries who retain the name of their respective country is "tourist".
People who have moved their lives to the United States are Americans (BTW, Mexico is in America, North America. Our country is named the United States of America); Americans (to use the colloquial) of foreign birth. Anyone, everyone who moves here with no intent of returning to live in the country of their birth is an immigrant, regardless of formal or casual entry into our borders. The argument that the persons of vague citizenship are a drain to the economy is stupid, considering the solution is so simple: get them full citizenship, get them on the public rolls, and tax them.
The actual name of "anchor Babies" is children.
Good G*D, do I have to think of everything??? (snark)