Aesop's fables vs allegory

Aesop's fables and allegory both are nouns.

Word	Noun	Adjective	Verb	Adverb
Aesop's fables	Yes	No	No	No
allegory	Yes	No	No	No

As nouns, allegory is a hypernym of Aesop's fables; that is, allegory is a word with a broader meaning than Aesop's fables:

Aesop's fables: a collection of fables believed to have been written by the Greek storyteller Aesop
allegory: a short moral story (often with animal characters)

Other hypernyms of Aesop's fables include apologue, fable, parable.

Aesop's fables (noun)	allegory (noun)
a collection of fables believed to have been written by the Greek storyteller Aesop	a short moral story (often with animal characters)
	an expressive style that uses fictional characters and events to describe some subject by suggestive resemblances; an extended metaphor
	a visible symbol representing an abstract idea