iirc the term "homeless" imply being a complete social outcast, while those people are in fact part of society often with jobs, families, friends etc. The only thing they lack is the physical house, therefore unhoused.
But as other posters noticed, the shift is also a liberal platitutide instead of action.
The shift wasn't initiated by liberals though, they are quick to adapt to new phrasing though if it means not having to take action that cost money as austerity rules supreme.
Yeah idk where it originated exactly, but the term itself suggest it was coined by someone actually having some empathy and brains, while liberals are famously lacking on both departments. Ultimately Engels is as always correct about the libs "These gentlemen think that when they have changed the names of things they have changed the things themselves."
Technically people who are couch surfing, sleeping in tents in campgrounds, or sleeping in garages or caravans are homeless as are people living in crisis accommodation. "Unhoused" lowers the statistic to just people without a roof over their head.
My take is it really doesn't actually do much (except perhaps reduce the sense of blame in the term homeless - i.e. unhoused implies they should be housed).
However chuds hate it because of that implication, therefore critical support for the semantic shift.
to a significant extent, it's the euphemism treadmill, but the usual argument i have seen is that homeless implies an inherent/permanent state of being while unhoused implies a more temporary one.
Standard lib response of "We won't actually change anything but we will change a word and act like it is a bigger deal than actually helping with your problems."
Houseless is a way to make homeless people roll their eyes and stop listening to you. If you want an excuse to not do effective work, then its as easy as using that term.