Simile: a figure of speech often comparing two unlike things. Usually introduced with the words "like" or "as"
example: The blade cut through her skin like a knife through warm butter.
Metaphor: a comparison between two things based on similarity and used as an actual substitute. Or as Aristotle defined it: giving a thing a name that belongs to something else.
example: Her eyes were blue sapphires.
There's actually a list of different types of metaphors over here at the OWL if you're interested.
The definitions for the these two words vary, but I think this quote sums it up best:
There's some differing opinions on which is best to use and why, but I think there's really only two things to remember when dealing with writing a metaphor or simile:
Make it clear is self-explanatory. You want the reader to form a clear picture of what you're describing. Comparisons only work when they make sense.
Avoiding the cliche is a little trickier. It requires time and serious thought to create awesome and original comparisons. But I've found a neat little brainstorming technique in Writing Tools by Roy Peter Clark.
*First, start with the cliched phrase. In Clark's example they use 'white as snow'.
*Scribble the phrase down on a piece of paper
* Start scribbling out some alternatives. (They don't have to be exactly what you're looking for. The key is to let your mind wander.)
white as snow
white as Snow White
gray as city snow
gray as the London sky
. . .
All of the alternatives might not be exactly what you're looking for, but you can always save the good ones for later. And by letting your mind stray, you'll be able to think outside of the box and produce some great comparisons that will make your writing engaging and entertaining.