There are several ways of dividing and thus defining homeless people.
Perhaps the most important way of dividing the homeless is between the group that becomes homeless only due to financial issues, and all the rest. For the person who has become homeless because he has lost his job/money, the road out of homelessness is fairly easy, he just gets another job. His homelessness is usually short term, and his homelessness happens only once in his life. (I use “his” because the overwhelming majority of homeless are men.)
Everyone else that becomes homeless does so because of some kind of mental, emotional, psychological problem that they are unable to cope with. These people usually become part of the “chronically homeless” population. Their homelessness can last indefinitely. If they escape homelessness it’s usually because someone from outside of homelessness bails them out and takes them in off the streets. These homeless people are also much more likely to experience more than one homeless episode, and become dependent on institutional life.