Metaphor is a figure of speech that compares without the use of as, like.
Simile uses as, like in comparison.
Examples in the poem:
All the world's a stage (world-stage)
And then the whining schoolboy, with his satchel,
And shining morning face, creeping like snail (schoolboy-snail)
And then the lover,
Sighing like the furnace (lover sighing-furnace)