I cited a single example of a state program while also saying there are other state, federal and charitable assistance programs. You don't like that example? Go find your own. There are plenty to choose from, likely in your home state. Example, if there is a public university in your state, undocumented folks are still eligible for financial aid. Check your state's eligibility rules for SNAP. Etc.
As far as migrants and refugees being "different": in a perfectly functioning system, I might agree with you. The US system is VERY far from perfectly functioning. One case in point:
https://www.nbcnews.com/politics/imm...e-us-rcna68687
What's also funny is that
WaPo's Kessler tried to fact-check a Mike Pence claim that 90% of migrants don't show up for their court dates. He ended up giving Pence 4 Pinnoccios, not because he could prove Pence's claim was factually wrong, but because Pence used data that Kessler deemed unreliable. Why was it unreliable? Because Kessler could find no hard numbers that any Federal bureau is tracking for the total number of failures to appear.
Or, if you're in New York and you need to demonstrate your eligibility for asylum, that's fine. However, you'll need to come back in 2033 for your hearing:
https://apnews.com/article/immigrati...a7f28231ff0edf
Bottom line: the legal definitions certainly specify a difference in the terms. You may be an asylum seeker when you cross the border. You're not a refugee until granted that status by a judge. You're PRUCOL, or something similar. In practice, the differences are far more difficult to parse because no one really has a handle on US immigration practices, neither the Border Patrol or ICE can keep up, Immigration Courts are backlogged, etc. There's also a brisk business in forged documents and identity theft in the mix. With all that wonderous diversity of mass uncertainly, I have zero confidence that federal or state benefit eligibility is being approved or denied with any level of consistency.
Its a mess, and I don't think anyone in DC has any idea how to fix it.