A metaphor is comparing two things without using the words like or as. Ex. She is dark, she is the moon. A hyperbole is something exaggerated. Ex. He was so hungry he ate a cow! A metaphor will most likely always be comparing two things.
A metaphor is a word or phrase that doesn't have a literal meaning eg:'He is a lion' meaning he gets angry easily. While a hyperbole is exaggeration in the description of something.