1. The difference is the weight. We teach the clean and the snatch as a jump because there is no other way to teach the necessary explosion. With an empty bar the feet will break the floor by several inches -- if they don't you are not jumping/exploding. When the load gets heavier, the air under the feet goes away and the lateral translation of foot position from pulling stance to catch/squat stance occurs just millimeters from the floor. A "donkey kick" is an incorrect attempt to emphasize the foot movement, when the feet break the floor as an artifact of the upward explosion. An intentional donkey kick always comes at the expense of force and acceleration on the bar.
2. A slam on the bar is a good way to emphasize the explosive aspect of the second pull. The bar doesn't travel forward because the mass of the body rotating back at the top of the pull reacts against the mass of the bar. If you hit your pubis when you do this in the snatch your grip is too narrow. Widen your grip until the bar touches you between pubis and ASIS when you are standing erect in the hang position. If you keep hitting the pubis, you are starting the second pull too early/low, and you fix this by waiting longer/aiming higher on your belly for the slam.