Think of the floor press as a box squat for your bench, so triceps fully on the floor and relaxed before exploding up.
I use a little leg drive but try not to cheat too much. Butt probably comes a little off the floor but not enough to walk under if you know what I mean.
As for comparing strength between the two: I am pretty close between the two as the bar comes quite close to my chest. I am probably 10kgs higher on floor press.