This is interesting. Two things can be true though. There may be a technical distinction between the two terms but I think many people (like me, until now!) don't know it, which means that many people do use it as a euphemism and not as its technical intention.

If I had a friend who was staying with us because he had no other place to be, he wouldn't be homeless. That's like saying my 13 yr old is homeless because his name's not on the mortgage. The only point of the euphemisms is for people to feel self-righteous for policing language. Which they often do because it's lazier than any sort of real reform.