Tramp: A person who travels from place to place, often without a permanent home or job. Historically, "tramps" were associated with wandering and working odd jobs to survive. The focus is more on being a traveler rather than a beggar. Bum: This term is often used to describe someone who avoids work and relies on others for survival. It can imply laziness or an unwillingness to contribute, although it’s sometimes used more loosely for people who are down on their luck. Hobo: Traditionally, a "hobo" refers to a migratory worker or someone who travels to find work. Unlike tramps, hobos are known for working wherever they go. The term originates from the early 20th century in the U.S. Beggar: This refers to someone who explicitly asks for money or food, often while living in poverty or homelessness. Begging is the central activity of a beggar, unlike a tramp or hobo, who might try to work or get by without asking for help directly.

I think the others covered the meanings pretty well. FYI, most of these are rarely used nowadays, at least in my experneice in the US. 'Beggar' is probably the most common. The others are kind of antiquated, at least in their original meanings. I'm not sure if hobos actually exist any more - or at least they're fairly rare. 'Tramp' and 'Bum' tend to be used in a more slangy way. Also, 'tramp' has a specific negative connotation when applied to a female. The current terms for these would be things like: Indigent person, homeless person, unhoused person, etc.

Given the choice to be either a tramp, bum, hobo, or a beggar, most people's first choice would be "hobo". It has a feeling of romance and adventure. Everybody's last choice would be "beggar". Absolutely nobody would want to be one of those. Their second choice would be "bum". It is a mild word. Some people even like to think of themselves as bums. There is even a joyful song, "Hallelujah, I'm a bum!", which you can find on the internet. Choice number three would be "tramp". It has many meanings, some worse than others but none are as unpleasant as "beggar".

Beggar has a different meaning as it requires asking for money. The other three are essentially obsolete in American English as far as housing status goes. ‘Bum’ is the most common but is most often used as a derogatory word suggesting low quality or otherwise having an obsession. My son’s high school friends are a bunch of bums. (Not good people) I really wanted to be a ski bum but I couldn’t bring myself to give up the handsome paycheck I got for coding.

They are synonymous with each other and some words, such as tramp and hobo are more American English as opposed to British English