story vs parable

story and parable both are nouns.

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

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

story (noun)	parable (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	(New Testament) any of the stories told by Jesus to convey his religious message
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