There is no real difference in meaning, UNLESS the person who is asking "Are you finished?" is using "finished" as an adjective that means 'out of energy or power' or 'without honor or prestige.' For example, "I am finished at the university" could mean "I am no longer welcome at the university" or "I no longer have status at the university." But if you're asking whether some is done with a task, then I would say that they're interchangeable. – Henry
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