People who are unhoused are not necessarily homeless. Their home could be their vehicle, a tent, a warehouse, or some other place. A home is a place you can come back to, where you can feel some modicum of security, belonging, or safety. A house is a structure, designed to be a home, but not always effectively so.
So I would argue that being unhoused is a more accurate description of many people's experiences and feelings than being homeless.