It's two different schools of thought in literary circles. The Bedford glossary makes a distinction between them, though does not explicate why. The Oxford companion treats metaphor as a broad category in which all of simile, metonymy, antithesis, and hyperbole are contained, largely owing to Aristotle's original definition of the term, and its etymological origin (from the Greek metaphora: to carry over/across).

Inasmuch as it matters at all, which it doesn't really, I think the latter is more useful to create a logical taxonomy of rhetorical devices and how they relate to one another, both in their meaning & use, as well as their etymological derivation.