story vs fairy tale

story and fairy tale both are nouns.

Word	Noun	Adjective	Verb	Adverb
story	Yes	No	No	No
fairy tale	Yes	No	No	No

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

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

Other hyponyms of story include cock-and-bull story, fairy story, fairytale, song and dance.

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

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
fairy tale: a story about fairies; told to amuse children

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