It signifies a placing of one thing beside another with a view OT comparison. The parable differs from the fable, by moving in the spiritual world, and never transgressing the actual order of natural things.
Fables teach human wisdom through fairy-tale like stories with speaking trees and animal.
Parables teach divine wisdom through realistic, true to life stories. A myth claims to be the truth itself, not a vehicle for truth like parables do. Myths confuse fantasy and reality. Modernists view the creation story, miracles and the resurrection of Christ as mythical fantasy stories. An allegory transfers the properties of one thing to another rather than comparing one thing to another.