club member vs fellow member

club member and fellow member both are nouns.

Word	Noun	Adjective	Verb	Adverb
club member	Yes	No	No	No
fellow member	Yes	No	No	No

As nouns, fellow member is a hypernym of club member; that is, fellow member is a word with a broader meaning than club member:

club member: someone who is a member of a club
fellow member: one of the persons who compose a social group (especially individuals who have joined and participate in a group organization)

Other hypernyms of club member include member.

club member (noun)	fellow member (noun)
someone who is a member of a club	one of the persons who compose a social group (especially individuals who have joined and participate in a group organization)