What is the relationship of allegory to fable?
One way to distinguish allegory from fable is to note that an allegory is a figure of speech used within a literary work and a fable is a genre or type of literary work.
An allegory is an extended metaphor in which one thing is described in terms of another. The difference between allegory and metaphor is that a metaphor can be any figure with a tenor and vehicle not using explicit comparison but an allegory normally is extended and has a narrative component.
A fable is a very short narrative, using traditional subject matter, normally framed in simple language and style, and often conveying a moral point.