Courteousey of CrossFit HQ
Squat clean aka Full Clean aka Clean = start from the floor, catch in a full squat.
Hang clean = start from the hang position (above or below the knees), catch in the full squat position.
Power clean = start from the floor, catch in a quarter or half squat position aka the power position.
Hang power clean = start from the hang position above or below the knees, catch in the quarter or half squat.
"Hang" describes where you start.
"Power" describes where you catch.