story vs allegory

story and allegory both are nouns.

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

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

story (noun)	allegory (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	an expressive style that uses fictional characters and events to describe some subject by suggestive resemblances; an extended metaphor
a short account of the news	a visible symbol representing an abstract idea
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