The force of a bat on a ball and the force of a ball on a bat are an unbalanced force or an impulse force.
Explanation:
If the bat is stationery and the ball is coming to collide with the ball with force, then the force exerting on the bat by the ball will break the bat. Similarly, if a moving bat collides with a ball, it will be an unbalanced force on the ball making the ball to set in motion.
Also a moving bat and moving ball colliding with each other will be exerting action and reaction on each other. The kind force will be an unbalanced force.
And for this reason only, the ball collided by the bat will fly in different direction after collision and the bat will remain in its place only. Thus, the bat's force on ball and vice-versa are an unbalanced or Impulse force.