fable vs parable

fable and parable both are nouns.

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

As nouns, fable and parable are synonyms defined as:

Other synonyms of fable include allegory, apologue.

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