Many think so, but they are different and overlap. Many think that if you have a roof over your head – housed that is (shelter, rooming house, somebody’s couch) then you are not homeless. They think you are homeless only if you live outside, on the streets. They are wrong.
“home is where the heart is” is quite valid and true. Just because a homeless person is in shelter or sleeping on a friend’s couch, or living in a cheap motel, doesn’t mean he or she is not still homeless.
They may be housed and homeless at the same time. This is a big issue and a terribly sore spot with the homeless. To them there is a world of difference; almost fighting words! There are homeless veterans and houseless veterans, two different levels of homeless, but don’t say that someone housed cannot be homeless. The houseless veteran is one that sleeps in a doorway or back alley or along some creek bank somewhere. The homeless veteran covers that and also the housed that cannot make a home out of their accomidations.
SOURCE: https://oldtimer.wordpress.com/2007/05/21/houseless-and-homeless-not-same-thing/