They are literally immigrants without citizenship. That phrase is 100% accurate, it captures everyone who is meant to be captured by it and doesn't capture anyone else.
The problem most will have with the phrase is the question of "whose fault is it?" that the choice of phrase leaves open. If you say "illegal immigrant" then it automatically assumes some criminal intent on the part of the immigrant. If you say "without citizenship" then it leaves open the question of "whose fault is it that they don't have citizenship?"
Citizenship is just a title. Don't ever delude yourself to think that you earned it, or that it is something that you deserve because of some virtue you maintain. There is no royalty is in the US.
On a related but independent note: (rant begins here)
How the hell is it your business if someone wants to live in the US? If they find a landlord who will rent to them and a job that will pay them, then it is absolutely no one else's concern. At most, it would be a zoning issue for counties trying to handle local population size. Even that is a stretch.
But in return for this paranoia, what have you gained? Suppose one day that you want to go live in France or Korea or somewhere else. Well guess what, you can't. Because they have the same policy you have, maybe in 10 years after you've given up tons of money and dignity, and then maybe you can somehow be treated as a second class citizen.
Thank god for you though, you have no intention of living somewhere besides where you were born. And you are totally fine living in this cage you've built for everyone.
If it became generally accepted that people should have the right to live in whatever state or country they want, this would be the single most important right any human would have. It would do far more to protect your other rights than even "Freedom of Speech" or "Freedom of Press", because when all else fails you can just leave to live with like minded people.
(end rant)