Q: vagrant とはどういう意味ですか?
A: A person without a home who wanders


Q: a vagrant と a vagabond と a hobo はどう違いますか?
A: Not much difference in UK English. Hobo sounds like slang, and is a bit unkind. Vagrant and Vagabond are quite uncommon words, I’m not even sure if they exactly mean “homeless person”, which is definitely what “hobo” means
Q: vagrants と rovers はどう違いますか?
A: vagrant = a homeless person who survives by begging
rover = a person who enjoys traveling without a specific destination in mind
Q: vagrant と peripatetic はどう違いますか?
A: Vagrant is generally used to mean a homeless person. It has less to do with travel.

No one uses the word peripatetic to describe a person. It is a rare word and one that not many people know. It will appear every once in a while in literature to describe a person who travels or wanders a lot, but I have never seen it used in conversation.