Mostly, the problem has to do with the laziness of the general citizen who throws around terms about homelessness interchangeably, as if they are only variations on the theme. (kinda like people accusing President Obama of being a Socialist and a Communist and a Nazi and a Muslim all at the same time) "Street People" are not necessarily homeless. Conversely, not all homeless people spend all their time living on the streets. If a person is couch surfing, they are not living on the street, but the home in which they reside is not theirs, and the arrangements made, so to sleep on someone's couch for a period of time are tentative at best.
Does living day to day at a rescue mission constitute a "home"? I have lived in the same place for over 4 years now. But I got this place by being in a program for the homeless. My case manager says I'm no longer homeless, but does this program make me not homeless? Or, is this just a homeless shelter with better amenities? When I lived in a halfway house for the homeless. It was a house owned and operated by a church that took in half a dozen homeless men. My residing there was conditional on my fulfilling certain requirements of the church. Did living there make me not homeless? Is there any difference between the house owned by the church, and the housing I have now - created by a government entity?
Paying rent doesn't seem to be an absolute definition of being homed, either. Most Salvation Army shelters charge the homeless for the right to spend the night there - about 10 dollars each night. Other shelters charge rent as well. Is having to work, do chores, etc., the same as paying rent?
Personally, I think the main consideration that should be made, as to whether a person is homeless or not, should be regarding societies reaction to a person's living situation. A person is not homeless when society accepts and allows for the situation in which people are living. If society gives its o.k., if the police do not harass the resident, if laws are not created so to discourage or inconvenience the person within their living arrangement, then I'd say the person was not homeless. This does not mean that a rescue mission or a shelter is a home. The administration and employees of such places work to get you out of those places as much as possible. So, shelters cannot be considered a home. Neither can living in a motor home, as there is no permanent place for a person to set their motor home. Most camping sites limit how long people can stay at the camps, usually only a couple months.
Only when society allows and accepts a person's living situation, free from any harassment, can that person be considered no longer homeless.