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Both are correct. Discharged is the more accurate and formal word. You can also say released. Released is considered a more informal, conversational word in this example.

thanks a million ways to die

Both are correct and perfectly fine to say. although discharged is grammatically correct when talking about hospitals. great question and well done. Hope this helps

In hospital terms, you would say "discharge. "Released" can be used if a prisoner was released from a jail.