He is a witch - and, like most witches in his world, wishes he wasn't. However, Chrestomanci reveals that Charles' magic is near enchanter-class, especially after examining the spell that Charles used to make Simon's every word become true.
He has invented a code for writing the school journals that everyone knows the teachers secretly read, so that he can accurately record things in innocuous-seeming entries. For instance, the code for "I've been having a bad day" is "I got up", which has the advantage that he can write it in nearly every journal entry without arousing suspicion.
see also: Witch Week (spoilers)