When referring to a promoter some authors actually mean promoter + operator; i.e., the lac promoter is IPTG inducible, meaning that besides the lac promoter, the lac operon is also present. If the lac operator were not present the IPTG would not have an inducible effect.
Another example is the Tac-Promoter system (Ptac). Notice how tac is written as a tac promoter, while in fact tac is actually both a promoter and an operator.