Error and mistake are similar. They are the thing that you do or make when you do something incorrectly. They are nouns. Error is a bit more formal, and more uncommon than mistake. 'You have made an error in your calculations!' 'Sorry, I made a mistake. I thought you were Samir'. Err is a verb - it means to make an error, and is somewhat historical. Nowadays it is mostly only used in a poetic context. 'To err is human, to forgive is divine'. Erroneous is an adjective, with a similar meaning to all the rest. It is also somewhat formal. 'There is an erroneous figure in your spreadsheet'. Wrong can be either a noun, or a verb, or an adjective. As a noun or a verb, it means to do something, (or the thing that you do) to somebody, that is unfair to them. Those are generally somewhat old-fashioned. He did her a grievous wrong when he left. You didn't need to wrong her like that. The much more common use is as an adjective. It means 'incorrect', or 'unsuitable'. 'You pushed the wrong button'. 'Those are the wrong trousers for your hair colour'. Fault is usually a noun. It can mean something like blame, or responsibility: 'It is my fault' (I made a mistake - I am responsible for it) Or fault can be a mechanical error: 'The fault is in your alternator'. (edit - fixed a mistake ;)