joke vs fool around

joke is a noun but fool around is not a noun.

Word	Noun	Adjective	Verb	Adverb
joke	Yes	No	Yes	No
fool around	No	No	Yes	No

As verbs, fool around is a hyponym of joke; that is, fool around is a word with a more specific, narrower meaning than joke:

Other hyponyms of joke include gag, quip, arse around, fool, horse around, pun.

joke (noun)	fool around (noun)
a ludicrous or grotesque act done for fun and amusement
activity characterized by good humor
a triviality not to be taken seriously
a humorous anecdote or remark intended to provoke laughter

joke (verb)	fool around (verb)
act in a funny or teasing way	indulge in horseplay
tell a joke; speak humorously	commit adultery