When people talk about the mind operating consciousness, they are referring to the conscious mind. That is why there is a term called ‘altered consciousness’. It means consciousness other than the conscious mind, such as the apha level.
A more complete way of seeing the operating consciousness is that it comprises both the conscious and unconscious.
Most people have a misconception that our mind operates on the conscious level. In fact, a large chunk of time while we are awake, we entered into the subconscious level. It is a two-way communication between the conscious and unconscious.