The difference between an analogy and a metaphor?

Many a time I've asked what the difference is between an analogy and a metaphor. I've asked it to my teacher, on internet sites, to my parents, so on and so forth. I got a different answer every time, and I never fully grasped what the difference is, so what is the difference?

Briefly, analogy is a perceived likeness between two entities; metaphor is one “figure of speech” which you might use to communicate that likeness.

For example: you may recognize that many Greek and Shakespearean tragedies have a similar structure: a phase of increasing conflict between opposed sides or characters, a major confrontation between the opposed characters, and a phase in which the opposition is worked out and resolved in one character's victory and the other's defeat.

It may then occur to you that this structure is very like the shape of a pyramid isosceles triangle, which rises from a baseline to a central point and then falls back to its baseline. You have then perceived an analogy betweeen a temporal phenomenon and a spatial one.

To communicate this analogy, you may employ metaphors. You name the central confrontation the “climax” —this is the classical name for a figure of speech, which is itself a metaphor: the word means “ladder”. You then name the first phase the “rising action” and the fourth stage the “falling action”.

Subsequently you perceive that the rising action has its own inceptive phase, when the characters and conflicts are introduced. These don’t fit so well into the triangular analogy, so you cast about for another analogy. One that occurs to you that of a public display of new works—so you employ the metaphor “exposition”. And for the final phase, when everything has “fallen” all the way back to the “baseline” you adopt the Greek word “catastrophe”, meaning “turn or fall down” or, metaphorically, “come to an end”.

And then you publish this elegant treatment of dramatic structure to universal applause, and the critical world pays you the ultimate honor of putting your own name on the basic metaphor: it becomes known to all succeeding generations as “Freytag’s pyramid”.

Most of those succeeding generations, however, find singular deficiencies in the model. They point out, for instance, that “exposition” of new facts occurs continuously throughout a play, and that many different actions occur alongside each other. They perceive a different analogy, that between dramatic structure and a tangle of threads; and to express this analogy they employ the metaphors complication (literally, a “folding together”) for the developing action and dénouement, a French word meaning “untying”, for the conclusion.

The analogy is what is expressed; the metaphor is how it is expressed.

Note, however, that metaphor is not the only way to express analogy. You may also employ simile: instead of talking about the analogous entity instead of the primary entity you may say that your primary entity is like the analogous entity. Or you can avoid language altogether and express the analogy in graphic form, using a labeled picture.

A metaphor is an implicit simile, while analogy is an explicit one. Put differently, a metaphor is literally false, while an analogy is literally true. Metaphors need a bit more imagination to interpret, while analogies are readily apparent.

"My cat is affectionate" is an analogy. You can literally see the cat shows behavior deemed affectionate. The comparison is straightforward, 1:1, between the cat's behavior and our idea of what "affectionate" looks like.

"My cat is a rock" is a metaphor. You can see literally the cat isn't a rock. The comparison isn't straight forward and asks us to imagine more so what it means to for the cat to be a "rock".

"My cat is an affectionate rock" is both, an analogy and a metaphor. "Affectionate" is apparent, while "rock" isn't.

I have often tried to conceptualize the difference, and here's my two cents.

Think of them this way: Analogy is a documentary. Metaphor is a fictionalization.

... which would make the above an analogy (I hope!).