A hobgoblin is a household spirit, appearing in English folklore, once considered helpful, but which since the spread of Christianity has often been considered mischievous. Shakespeare identifies the character of Puck in his A Midsummer Night's Dream as a hobgoblin.
A fairy is a type of mythical being or legendary creature, generally described as anthropomorphic, found in the folklore of multiple European cultures, a form of spirit, often with metaphysical, supernatural, or preternatural qualities.
1888 illustration by Luis Ricardo Falero of common modern depiction of a fairy with butterfly wings