I can't get it to post from the lock mode but it's the same background

As I age, it would be nice if that skeleton would chill out and stop creaking and aching.

It ultimately just comes down to preference I reckon. And as long as you're coming at it from a place of empathy and respect, no one acting in good faith is going to give pushback.

That's fair to say (the distinction between home and house).
I imagine there are some folks who prefer the term homeless, too. The ones I work with seem to largely favor unhoused, though.
There are even some who assert that they have a home (wherever they're camping), but not a house.

From several unhoused friends, they prefer the term because it (rightly) recontextualizes the problem as a systemic one rather than a personal one. Homeless implies they are responsible for their lack of home. Unhoused suggests that society is allowing people to live in the elements.