parable vs fable

parable and fable both are nouns.

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

As nouns, parable and fable are synonyms defined as:

Other synonyms of parable include allegory, apologue.

parable (noun)	fable (noun)
a short moral story (often with animal characters)	a short moral story (often with animal characters)
(New Testament) any of the stories told by Jesus to convey his religious message	a story about mythical or supernatural beings or events
	a deliberately false or improbable account