Both draw power from the lower half. Both need direction towards their target; Pitcher striding towards the catcher and the Hitter striding towards the Pitcher. Both use the hips to generate torque for the upper half to come through. Both need the upper half to stay closed as long as possible (until the stride foot hits the ground) for your upper half to come through with the most whip possible. They are both very similar to one another.
Use video analysis to see where their body position is at front foot contact. In the swing, nothing should start to the ball until their stride foot make contact with the ground, just as in the pitching delivery, the upper half should be in a closed, front arm up at shoulder height and ready to fire, position when their stride foot hits the ground.
Players starting with their upper half too soon is a very common problem in hitters and pitchers. When we do this, we are giving up power and using too much upper body too soon to throw or hit the ball. With a pitcher especially, this puts unnecessary stress on their arm.
Help your players learn to be in a powerful position when their stride foot hits the ground. If they start their upper half towards the plate, or ball, too soon, help them learn to keep it closed longer. Have a hitter stride, hold it for a second, to make sure they are in a strong position before they swing. Have a pitcher get to his stride and freeze at front foot contact to see where their upper body is and where we want it to be. This is a simple drill for them to feel that power position.
Hope some find this helpful as this is one of the most common mistakes I see young players making.