joke vs funny story

joke and funny story both are nouns.

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

As nouns, funny story is a hyponym of joke; that is, funny story is a word with a more specific, narrower meaning than joke:

joke (noun)	funny story (noun)
a ludicrous or grotesque act done for fun and amusement	an account of an amusing incident (usually with a punch line)
activity characterized by good humor
a triviality not to be taken seriously
a humorous anecdote or remark intended to provoke laughter

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