In the US they mean different things, as homeless includes people living in other people’s homes. That can include people whose house just burnt down and are living with friends or family because they lost their permanent residence (home). Unhoused is about where they are staying.
People on the street are homeless and unhoused.
And you really think people use and understand these terms like that?
You may be correct in the academic sense, but completely wrong in all other senses.
Are you suggesting that the incorrect terms should be used to cater to those of you that don’t know there is a difference? Even if you were unaware that there is actually a difference, was the intent and meaning of the headline lost in confusion, or did you understand exactly what they meant?