What Is The Difference Between A Simile And A Metaphor?

A simile is an image which works by comparing two things using the word "like", "as" or "than." "My love's like a red, red rose" is clearly more than just a straightforward comparison along the lines of "A parsnip is like a white carrot." In a simile, the purpose of the comparison is to create a picture in which the two subjects are linked in the reader's mind; so Robert Burns' beloved is associated with ideas of sweetness, fragrance and so on.
A metaphor takes the comparison further. The word means "carrying over" and in a metaphor the two things are joined together; one actually becomes the other, rather than being compared to it. In" Hamlet", for instance, Hamlet is urged to "cast thy nighted colour off," nighted being a metaphor to describe his black mourning clothes. Here no explicit comparison is made, but a connection is set up between Hamlet, darkness and death, which is a recurring idea in the play.