As nouns the difference between axon and anon
is that
axon is a nerve fibre which is a long slender projection of a nerve cell, and which conducts nerve impulses away from the body of the cell to a synapse while
anon is an anonymous person, especially an author.
As an adverb anon is
straightway; at once.
As an adjective anon is
anonymous.
As a proper noun Anon is
the name given when an author's name is unknown.