What is the difference between a symbolic poem and an allegory?

A symbolic poem, by which I imagine you mean a poem that
uses symbolism, is exactly that, a poem that makes use of various symbols to represent
various ideas or feelings.  An allegory, on the other hand, whether a poem, a story, or
a novel, is a complete story, told on two levels, one being the literal level, the story
that is being told, and the other being the level in which the entire story acts as a
symbol of the point being made.  Orwell's Animal Farm is a good
example of an allegory, being a story about the animals and also representing Stalinist
Russia.  C.S. Lewis' Chronicles of Narnia is a series of allegories
representing Christian ideas, stories that operate very well as stories,
too.