What is a poem what are three differences in poems and fables?

A Fable is just another Word for 'story'.

Usually when we talk about 'Fables' we mean 'a story with some kind of a moral lesson'. Aesop's Fables are typical Fables; and a story such as The Dog and the Bone has an obvious lesson to teach.

Quite often Fables will have some element of magic or fantasy; and almost as often a Fable will have animals who can talk and think like humans as main characters.

But these things are not necessary. Many fables are fantastical, or have animals as characters; but a fable such as Neruda's Mermaid and the Drunks delivers its moral lesson in an almost realistic narrative.

A Fable can be a poem (Dryden and La Fontaine both wrote famous fables which are also poems); but it does not need to be (Aesop's Fables are often found as prose stories; and so are the fables in the Arabian Nights).