Swinging: You're pretty much letting your pivot do all of the work and letting centrifugal force square up the face for you. However it isn't a "pivot controlled hand" stroke because you still have your minds in your hands. You know that you have have your hands ahead, with a flat left and a bent right. Brian explains this with his "pivot powered hand control" designation. Also, in swinging, your hand TURNS to the plane, and cocks up the plane. Then it un-cocks DOWN the plane, rolls BACK to the plane (with a slightly open face at impact), releases to square, the ball leaves the face, then the left arm ROLLS back to the plane and re-cocks up the plane. That's swinging in a nutshell. The big difference is you UN-COCK THEN ROLL...it is a SEQUENCE. No roll then un-cock if you're a swinger. That's bad news.
Hitting: You are trying to not let the club/hand turn to the plane. You are trying to take it away with the face looking at the ball. However because your body is turning, somewhere near the end your arm is going to turn to the plane. However the "feel" is that your pp#3 sweet spot pressure point is still BEHIND THE SHAFT. Not "under it" like a swing would feel. Now a hitter SIMULTANEOUSLY un-cocks AND rolls into the ball and begins to CONSCIOUSLY straighten that right arm into the ball, but you MUST KEEP A BENT RIGHT WRIST. Thats hitting in a nutshell.
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Now before i get flamed, i know i left a lot out...but this is the basic concept. If you'd like to see this more in a video. Check out Brians video short on "Hitting vs. Swinging." He demonstrates everything i just said.
Also, this may help. Imagine you are going to karate chop someone in the throat. Now instead of doing that to someone in the throat, you are that to the inside corner of the ball. That is the "feel" for swinging. You are pulling with that left side and karate chopping that ball. In Hitting, imagine you are going to punch someone dead straight in the chest with the bottom part of your palm. To do that with any power you'd need to have your hand bent back towards your forearm so it is "braced" for that punch. Now instead of doing that to someone in the chest, you are going to do it to the GROUND!
Hope that helps...