The Hitter's Clubshaft acts as an Axe Handle that he Pushes radially (from behind) through Impact. The Swinger's Clubshaft acts as a piece of rope -- the Rope handle -- that he Pulls longitudinally (lengthwise) through Impact.
Remember, you can push on the Axe Handle, but...
You can't push on a rope handle.
But you can pull on an Axe Handle, can't you? I always wonder why this never gets mentioned.