fairytale vs story

fairytale and story both are nouns.

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

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

fairytale: a story about fairies; told to amuse children
story: 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

Other hypernyms of fairytale include narration, narrative, tale.

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

fairytale: an interesting but highly implausible story; often told as an excuse
story: a trivial lie

Other hypernyms of fairytale include fib, tale, taradiddle, tarradiddle.

fairytale (noun)	story (noun)
a story about fairies; told to amuse children	a structure consisting of a room or set of rooms at a single position along a vertical scale
an interesting but highly implausible story; often told as an excuse	a piece of fiction that narrates a chain of related events
	a short account of the news
	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