There are many literary terms that are so closely related but are not the same. The word allegory is a lot like the word symbol because it's function is to represent. However, the difference between the two is that an allegory is a group of symbols that work together.
Napoleon symbolizing Stalin, Snowball symbolizing Trotsky, Boxer, the working class; Mollie, the vain; Mr. Jones, the Romanovs or Nicolas II; Manor Farm, Russia; and the Rebellion, the Russian Revolution. This group of symbols makes up the entire allegory.
This is similar to metaphor and extended metaphor if you know that concept.
Really, this whole book is an allegory. Remember, an allegory is like a long metaphor. In an allegory, something is being used to represent something else. In this case, the characters and events are allegories for things that happened in Russia and the Soviet Union.
For example, the horse Boxer is an allegory for the working class of the Soviet Union. He works hard and is completely dedicated to Napoleon (himself an allegory for Stalin). Napoleon works him basically to death and then, essentially, sells his carcass for money. This represents Stalin's ruthless exploitation of the working class in the Soviet Union.
An allegory is an extended metaphor in which a series of symbols work together to create a specific parallel between the actual story and its deeper meaning. In Animal Farm, Orwell creates a story about animals and their relationship with humans; this narrative specifically parallels people and events of the Russian Revolution.
Old Major’s invention of Animalism represents Karl Marx’s invention of Communism. Both Marx and Old Major recognize the power of the working class and envision a time when the working class will be rewarded for all that they contribute to their government and/or farm. Napoleon’s abuse of power and distortion of Animalism mirrors Stalin’s misuse of Marx’s ideals. Boxer is the working class itself: he kills himself in service to a government that exploits him. Orwell believed that the Russian Revolution yielded the same results.