Similes and metaphors are actually related to one another.  A simile is one type of metaphor, but metaphors are not similes.
A metaphor is considered the broadest of the two. It is a literary device category that passes the meaning of one thing to another. An example of a metaphor: She is the black sheep of the family. While she is not a black sheep, she has characteristics that are similar to the black sheep.
A simile, while essentially the same thing, typically has the words "like" or its equivalents or "as."  It is considered much more direct when comparing unrelated items.  An example of a simile: She is as graceful as a swan. While she is not a swan, it is stated that she possesses the same grace as one.