No.

There’s a terminology conflict here. A fairy tale is a fantastical adventure, set in an indistinguishable far-off place and time, in which a good character goes through hardship and comes out with a good/happy ending.

A fable, such as Aesop’s fables, is likewise a fictional tale, but is usually shorter and does illustrate a moral point.

For example, the Androcles fable illustrates that “Gratitude is the sign of noble souls”; or the fable of the Mischevious Dog illustrates that “Those who achieve notoriety often mistake it for fame.”