The word translates from the Greek as simply "change of shape", but in English it has always implied radical change – from one kind of being to another. Western myths in general, and Ovid's Metamorphoses (written circa AD1-8) in particular, further suggest that, when something or someone has undergone metamorphosis, the event must have occurred through Magic.
Fantasy uses a variety of terms for changes of shape and nature. In this encyclopedia's taxonomy, metamorphosis has the old meaning of magical and radical change experienced by the subject, who may well have initiated as well as lived through the process; such change can be involuntary and/or inherent in the subject's nature. The keys to Shapeshifting are reversibility and repeatability, as seen when Werewolves change with each full Moon. Transformation implies and emphasizes an external agent of change: the Frog Prince is transformed by a Witch. Transmutation concerns changes in the nature of inanimate material.
The active/passive distinction between metamorphosing and being transformed is too easily blurred to be a rigid dividing line. Tallis in Robert Holdstock's Lavondyss (1988) painfully metamorphoses into a tree; or perhaps she is transformed by the magic of the heartwoods. The nymph Daphne is transformed into a laurel to save her from Apollo's pursuit; but the change can be read as a chosen metamorphosis. In a world of magic, any transforming action of the gods may be as "natural" a metamorphosis as the (evidently god-mediated) change from caterpillar to butterfly.
Thus, in Fantasy, metamorphosis tends not to be arbitrary. Often it reveals the real nature of the subject, as with Arachne – the prideful weaver whom Athene transformed into a Spider – or the protagonist of Franz Kafka's Metamorphosis (1915), who awakens one morning in the shape of a cockroach. (In both cases metamorphosis can be understood, in terms of Jungian Psychology, as a triumph of the Shadow.) It may represent a Rite of Passage or constitute a release from Bondage: being taken into a princess's bed fulfils a Condition and frees the Frog Prince. But however a metamorphosis can be understood – whether longed-for or abhorred by the subject – it does not happen by accident: it comes from the nature of the subject. An abhorred metamorphosis is likely to have generated the Story; a longed-for metamorphosis is likely to resolve the Story through a Recognition of the true identity of the protagonist. [JC/DRL]
see also: Beauty and the Beast.