Can someone explain to me how these two are different? And I'm talking more than just a dictionary answer, because I could do that on my own.
I only ever hear conceit in use concerning poetry, which is the bane of existence and much be purged from the human experience before it destroys our souls. A conceit is a form of metaphor and does not have to refer to a specific event. Allegory is where a story is symbolizing a particular event in real life. For example, Tolkien was often stressed that people considered the Lord of the Rings as one big allegory for World War II. He preferred applicability, the ability of a work to have different meanings to different readers and various times.