I'll start you off with some examples:
Simile: "Her eyes were like small galaxies, enchanting in themselves"
Metaphor: "Her eyes were small galaxies, enchanting in themselves"
See the difference?
All similes are metaphors, but not all metaphors are similes. Like that rectangle thing. A metaphor is a comparison, and a simile is a type of metaphor that uses "like" or "as" to compare things.