Idiom: An idiom is an expression
that conveys something different from its literal meaning, and
cannot be guessed from the meanings of its individual words.
"Between a rock and a hard place" is an idiom that means “in a
difficult or bad position with no good way of getting out of
it.” What makes an idiom different from a figure of speech is
that its non-literal meaning is already familiar to speakers of
the language.
Metaphor: A metaphor is a word or phrase typically used to
describe one thing, but unexpectedly used to describe something
different. Metaphors make language interesting and help create
imagery. "He was drowning in paperwork" is a metaphor that makes
a connection between having to deal with a lot of paperwork and
drowning in water.
Simile: A simile is an expression that uses the words like or as
to describe something by comparing it with something else. A
simile is like a metaphor except that a simile uses the words
like or as to signal that a comparison is being made. “She is as
fierce as a tiger” is a simile, but “She is a tiger when she is
angry” is a metaphor.