What is the difference between metaphors and a simile?

A SIMILE is a phrase that describes something in comparison to the characteristics of something else, using the Words as or like.

Examples: Her hands were as cold as ice. His beard was like sandpaper.

A METAPHOR directly compares two things, which may be quite different, because one has a characteristic that is similar to the other.

Examples: All the world is a stage. The inside of the car was a furnace. His memory of the event was foggy.

Sometimes metaphors compare actions and adjectives by their effect.

Examples : He was boiling mad. You are the sunshine of my life. The truth was hard to swallow.

In many cases, a metaphor is an idiomatic expression when it suggests an improbable action, e.g It was raining cats and dogs. He was rolling in dough.