Fable

Fable is a literary genre: a succinct fictional story, in prose or verse, that features animals, mythical creatures, plants, inanimate objects, or forces of nature that are anthropomorphized (given human qualities, such as verbal communication) and that illustrates or leads to an interpretation of a moral lesson (a "moral"), which may at the end be added explicitly as a pithy maxim.

A fable differs from a parable in that the latter excludes animals, plants, inanimate objects, and forces of nature as actors that assume speech or other powers of humankind.

Usage has not always been so clearly distinguished. In the King James Version of the New Testament, "μῦθος" ("mythos") was rendered by the translators as "fable" in the First Epistle to Timothy, the Second Epistle to Timothy, the Epistle to Titus and the First Epistle of Peter.

A person who writes fables is a fabulist.

https://en.wikipedia.org/wiki/Fable