THIS IS HORRIBLE ADVICE FOR ANY ADULT LEARNING TO PLAY THE GAME AND WILL DO NOTHING BUT SCREW YOU UP. However, if you're looking for the reason why pros generate more distance, it's simple physics of force. They have trained themselves to make a really hard swing at the ball, smoothly and efficiently. Paradoxically, the best way for most people to increase clubhead speed over time is to focus not on clubhead speed, but on a smooth and efficient swing that stays on a simple plane. If you eliminate elements of the swing that are inefficient, you actually increase the force, without increasing the effort and you do so on a plane that keeps it in control as well.
It is generally assumed that 1 mph of swing speed increase = 1.5mph of ball velocity increase = 2.5-3 yards of carry distance increase. I think TW swings about 125-130 and a long-drive competitor around low 140s.
Not sure how fast Happy Gilmore's SS was.