They are synonyms. Please don’t make things up.

Edit: to all the knee-jerk downvoting. This is literally a quote from an article the user himself supplied as proof that there is a difference.

Unhoused is probably the most popular alternative to the word “homeless.” It’s undoubtedly the one I see most often recommended by advocates. But it doesn’t have a meaningful difference in connotation from the more common term, “homeless.”

It’s literally just a pc synonym of homeless.