In the world of English as a second or other language, a mistake is something you got wrong that you knew was wrong after the fact; e.g., the typo in *I loke chocolate. Correction: I like chocolate.
An error is something you got wrong that you didn't know was wrong after the fact; e.g., a student's sentence, *I have seen him yesterday. Correction: I saw him yesterday.
The word fault has more than one meaning. Click here. Let us know which meaning you are having trouble with and the context or situation you'd like to use it in.