Simile: Using “like,” “as,” or “than” for a comparison between two things which seem to have nothing in common.

The branches of government are like internal organs in the body.

His hatred ran as deep as an ocean.

Doing homework is easier than digging ditches.

Metaphor: a comparison between two things which seem to have nothing in common. Metaphors do not use “like” or “as” in the comparison.

His bad attitude just added fuel to the fire.

Talent scouts are always looking for someone  
who is a diamond in the rough.