What do you call stories with morals?

What do you call stories with morals?

It could be a fable or a parable.

Fable= story that teaches a moral lesson/principle, but often times uses animals or inanimate objects to carry the message through.

Parable= story that teaches a lesson, but uses human characters.

Example of parable- 'The Boy Who Cried Wolf'
Example of fable- 'The Tortoise and the Hare'