Metaphor, n.
Etymology: [F. métaphore, L. metaphora, fr. Gr. meta beyond, over + ferein to bring, bear.]
(Rhet.)
The transference of the relation between one set of objects to another set for the purpose of brief explanation; a compressed simile; e. g., the ship plows the sea. Abbott & Seeley. "All the world's a stage." Shak.
Note: The statement, "that man is a fox," is a metaphor; but "that man is like a fox," is a simile, similitude, or comparison.
Shades of meaning
Fernald has no entry of its own for metaphor; he lists it under allegory.
Where he writes about it:
In modern usage we may say that an allegory is an extended simile, while a metaphor is an abbreviated simile contained often in a phrase, perhaps in a word. — from allegory
The simile carries its comparison on the surface, in the words as, like, or similar expressions; the metaphor is given directly without any note of comparison. — from allegory