The additional technical element for the power clean from the floor versus the lift from the hang is the passage from below the knees to above the knees. What needs to happen is that you initiate the pull from the floor with the hamstrings.
Power Clean From the Floor
You do this by moving the knees back so that when the bar reaches the knees, the tibias are perpendicular to the floor. While you're doing this, the bar is kept close to the body so it's lifted in a slight backward arch.
When the bar reaches the upper third portion of the quadriceps, explode upwards with the legs, hips, and lower back. Focus on "standing up as explosively as possible."
Avoid pulling with the arms too early and don't accelerate until you pass the knees. The biggest mistake people make is starting too fast off the floor. Notice that the feet leave the floor, but it's not an upward jump; it's a lateral re-adjustment of the stance width.