Today, the words are generally irrelevant by their original definitions and the homeless are typically just called homeless people or hobos. Today, we typically use “bum” to refer to a lazy, jobless person who lives at home, and use “tramp” as a denigrating term for a woman.
The overarching term for these is “vagabond,” which we seldom hear at all now. By the proper definitions, though, a hobo is a worker with no home who goes from place to place looking for work. Hobos were typically the homeless people that would try to catch rides on trains. A bum, unlike a hobo, is a vagabond who rarely looks for work, or has very little worth ethic.
A tramp is similar to a bum, but only works when forced to. Another interesting fact about hobos is the “Hobo code.” If you’ve seen Mad Men, you likely know about it already.
During the Great Depression, hobos developed a code to mark homes or establishments one of many ways to tell other hobos if they should leave, should request work, could get free medical aid, etc. You can check out the Hobo code here: