While both "error" and "mistake" refer to a wrong action, there is a difference between them in usage and connotation. A mistake in general is a choice or a misjudgment or a miscalculation that led to a "wrong" action. For example: " I made a mistake in the second question of the exam." or " Coming to this restaurant was a huge mistake; the food is disgusting" Error is more formal and generally refers to something that is "wrong" because it does not fit into the "right" or "normal" conditions. For example: "The computer is showing an error with that file"

They're synonyms. But, the difference is in the context that they're used in. Mistake = Accidental (when you know that something was/is wrong) Error = Lake of knowledge (it's more formal than mistake)