Buddy, chum and pal are essentially quite similar, meaning close/intimate companions/friends, while fellow has a couple of different meanings of which some of these you may be interested in: 1) a person 2) a companion 3) a person belonging to an equal rank in work/equivalent situations 4) informally used to refer to someone's beau/boyfriend/suitor 5) a man or a boy 6) used in education to denote membership in some educational institutions/societies or a researcher who has obtained funding for research etc

Very little difference. Fellow is a but old-fashioned but the others mean the same thing. Other similar words are: mate, mucker, fella, china and fruit. China is rhyming slang for China Plate - meaning mate. Fruit is rhyming slang for fruit gum - meaning chum. My examples are mainly used in the UK.

Fellow is informal for a member of a social circle. Kleo Ng gives some of the formal meanings of fellow. Buddy, chum and pal are informal words for friend. All three of these mean friend, but they are all somewhat outdated. More contemporary words in American English include 'bud' (yes, it's a short version of 'buddy'), and 'amigo,' which is borrowed from Spanish. But the most common word is still 'friend.'