So what's the difference between a metaphor and a simile? They both serve the same purpose and act an an analogy between two things that are, by all means, not alike.
The cloud was as puffy as a cotton ball.
The cloud was a cotton ball in the sky.
The cloud was like a cotton ball.
But which is which? A metaphor compares two unlike things without using "like" or "as". Both of these words indicate you're looking at a simile. So in the example above, the middle phrase The cloud was a cotton ball in the sky is the metaphor. The other two are both similes.
Metaphors tend to be more vague, requiring the reader to infer more into the meaning, while a simile is supposedly more specific.
For example, you can use a simile to express irony:
Her feet were as fast as cement blocks.
However, the same idea with a metaphor is relatively not as clear, and certainly not at all ironic:
Her feet were cement blocks.
While it may not really matter which is which since they both serve a similar purpose in the end, it can be nice to know the difference at dinner parties if you plan on impressing your friends!