Satyrs have the upper body of a human and the lower body of a goat. Not to be confused with the Faun. Most people believe that they are the same when in fact, they are not. It is mostly how they came to be that makes them different but there are many facts that make them different. For instance, while a faun is born with horns, the Satyr must earn them.
Fauns are known to be gentle, beautiful (or handsome) creatures where as the satyr is known to be clumsy and hideous.
For reference, Clover from the Percy Jackson series is a Satyr. Mr. Tumnus from The Chronicles of Narnia is a faun. (Clover may not be the best reference as of he is not particularly hideous.)