A simile is a figure of speech in which two essentially unlike things
are compared, often with a phrase introduced by like or as:
teeth are like pearls.
He's white as a sheet.
"A deferred dream dries up like a raisin in the sun." (Langston
A metaphor implies a comparison between otherwise dissimilar things without
use of like or as:
"All the world's a stage." (Shakespeare)
She's so shy. She's a little mouse.
By marrying her, he's embarked on a sea of troubles.
An analogy is a type
of comparison. It compares objects or ideas from
different classes - things not normally associated. The word analogy refers
to a whole idea or paragraph; the analogy itself may contain similes and/or metaphors:
was so sick. My head felt like a battered soccer ball, and the nasty flu was
the home team trying to score a goal with it.