A mistake refers to an error in a belief or decision. It does not imply something immoral. "Wrong" can also refer to such an error. However, it can also mean some action or belief that is not correct morally. If I add 15 plus 16 and get 35, the answer is mistaken. It is also wrong. If somebody steals something, it is not mistaken. The person intended to steal it and did. We can, however, say that he is wrong to steal. In this case, a moral judgement applies.