You are talking about two different things.
The term hang tells us where the lifts starts.....it starts in the hang position. This can be above the knee, below the knee or mid thigh.
The term "power" tells us where the lift ends. If you catch the bar in a quarter squat position, then it is a power clean. if you catch the bar at a 90 degree or deeper squat, it is a full clean (or a squat clean). You will use less weight on a power clean because you are pulling the bar high enough to receive it in the quarter squat position.
You can do a power clean from the hang position. You can do a full clean from the hang position. You can do a power clean or a full squat clean from the floor too.
Terminology man.