Simile is a comparison between two things using special comparison words like, as, resembles, or than.
A metaphor makes an implied comparison; basically, a metaphor says that something is something else.
For example,
"Bill is as sly as a fox." It is a simile. It is using comparison words as ... as.
"Bill is a sly fox." It is a metaphor. No comparison words are used; it is an implied comparison.