funny story vs joke

funny story and joke both are nouns.

Word	Noun	Adjective	Verb	Adverb
funny story	Yes	No	No	No
joke	Yes	No	Yes	No

As nouns, joke is a hypernym of funny story; that is, joke is a word with a broader meaning than funny story:

Other hypernyms of funny story include gag, jape, jest, laugh.

funny story (noun)	joke (noun)
an account of an amusing incident (usually with a punch line)	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

funny story (verb)	joke (verb)
	act in a funny or teasing way
	tell a joke; speak humorously