I have not yet been homeless, thank God, but I do sympathize with those who fall on hard times and don't have the support system of friends and family to help get them back on their feet (I had that and that's the only reason I was never homeless).
One other preconception is that there are beggars who will stand at busy intersections and ask for handouts. I think many of these are scammers and not legit homeless people in need of help. Maybe there are some real homeless victims amongst them, but you really can't ever know, and perhaps they give people in real need a bad name.
I left that one out because "scammers " are not "homeless" and therefore it is not a "preconception about the homeless".
You are right, they're not the same, but I think that many people make that connection in their minds though. :(