A short moral story (often with animal characters) WordNet 3.0 & Open English WordNet

Fable is a literary genre defined as a succinct fictional story, in prose or verse, that features animals, legendary creatures, plants, inanimate objects, or forces of nature that are anthropomorphized, and that illustrates or leads to a particular moral lesson, which may at the end be added explicitly as a concise maxim or saying. Wikipedia

An apologue or apolog is a brief fable or allegorical story with pointed or exaggerated details, meant to serve as a pleasant vehicle for a moral doctrine or to convey a useful lesson without stating it explicitly. Wikipedia

Story intended to illustrate a moral. Wikipedia Disambiguation

Short fictional story that often anthropomorphises non-humans to illustrate a moral lesson Wikidata

Brief fable or allegorical story with a useful lesson or moral doctrine Wikidata

A symbolic representation which can be interpreted to reveal a hidden meaning, usually a moral or political one. Wiktionary

Symbolic representation. Wiktionary (translation)

A short story with a moral, often involving talking animals or objects; a fable. Wiktionary

A short story with a moral, often involving talking animals or objects. Wiktionary (translation)

A fictitious narrative intended to enforce some useful truth or precept, usually with animals, etc. as characters; an apologue. Prototypically, Aesop's Fables. Wiktionary

A short narrative illustrating a lesson (usually religious/moral) by comparison or analogy. Wiktionary

Short story illustrating a lesson. Wiktionary (translation)