In their literal senses, 'finished' and 'done' have different meanings. However, in informal and colloquial language, particularly in American English, 'to be done' is sometimes used as a synonym of 'to have finished'. 'Are you done?' can be used to mean 'Have you finished?' or 'I'm done with this' means 'I've finished with this'. The reverse doesn't happen - or in other words, you can't use 'finished' when you actually mean 'done'.

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You will find many English speakers who do not correctly use the word finished. Here is the correct meaning of both: "Finished" is the end of something: Class is finished. I am finished writing. I am finished trying. "Done" relates to cooking (in the sense you are asking): The chicken is done. Is the meat done?