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It's a beautiful expression from The Tempest - Ferdinand's father died in a storm at sea, and Ariel sings a song to comfort him, telling him that his body has been changed by the sea into a beautiful and precious object. So it refers to a gradual change, where the form's the same, but the substance is different (and maybe more precious and beautiful?): ""Full fathom five thy father lies, Of his bones are coral made, Those are pearls that were his eyes, Nothing of him that doth fade, But doth suffer a sea-change, into something rich and strange,"
...and so a bit disappointing when people use it to refer to something being 'a bit different'.