I'm not a lawyer, but I did take vocabulary and grammar in grade school.
A "non-citizen" can also be a legal immigrant with temporary status, legal resident status, greencard, refugee officially granted asylum status. So many "non-citizens" can still be legal residents.
"Illegal" - aliens, immigrants, non-citizens - are "illegally" in the United States in violation of immigration "laws". Breaking laws also makes one a criminal. Maybe, instead of calling them "illegal" whatevers we should refer to them as "criminal" whatevers because their presence in the United States is a crime, or adjectively "criminal".
They can't be "immigrants" because that implies compliance with established immigration laws.
How about "criminal trespassers"?