story vs fable

story and fable both are nouns.

Word	Noun	Adjective	Verb	Adverb
story	Yes	No	No	No
fable	Yes	No	No	No

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

story (noun)	fable (noun)
a structure consisting of a room or set of rooms at a single position along a vertical scale	a short moral story (often with animal characters)
a piece of fiction that narrates a chain of related events	a story about mythical or supernatural beings or events
a short account of the news	a deliberately false or improbable account
a trivial lie
a message that tells the particulars of an act or occurrence or course of events; presented in writing or drama or cinema or as a radio or television program
a record or narrative description of past events