To further clarify, a tramp is someone who travels around but works only if/when he has to, a hobo is someone who travels around mainly looking for work and a bum is someone who does neither.
This is news to me, but a neat distinction. American English, I presume, since the latter two are unknown in English usage, unless they've just become archaic and associated only with American (see "soccer"). I suspect these nuances have been lost to most, but then that's a common problem in modern usage.
We don't really see tramps anymore in the UK. Your definitions are correct. A tramp is someone who is always on the move. We saw lots of them after the two world wars in the UK, as conscripted traumatised ex servicemen returned home. I'd imagine in the USA to see a few Vietnamese War veterans to be tramps now.
About twenty years ago, while day-hiking in the southern part of the Peak District, I got talking to a guy who was walking the same section of road as me. He was pretty shabbily dressed and his shoes were worn-out, and he said he was walking from (I think) Birmingham to Carlisle to stay with his brother because he had no money and nowhere to live. He told me he was keeping away from towns and sleeping in forests and barns. All his possessions were stuffed into the pockets of his coat. We walked a couple of miles together and he seemed like a nice guy.
Not exactly a "gentleman of the road" with a spotted-hanky-bundle on a stick, but the nearest I've seen to an archetypal tramp. I hope he made it.
I originally used the word "tramp" because (from memory) that was the word Orwell used to describe himself in Down and out in Paris and London; corresponding to the meaning described at [1]. I was aware that it is considered pejorative, but not the different meaning in US English.