Double witches and double wizards are fantasized super-witches (resp. wizards) that would be to regular witches as witches are to muggles. Some young witches and wizards believe in double witches.
In 1992, S.P.H.E.W. members think Susan Bones is a double witch after she beats bullies with spells much too powerful for a first-year. In this case "Susan Bones" is in fact 7th-year student and metamorphagus (canon) Nymphadora Tonks impersonating the real Susan to protect the S.P.H.E.W.