(A)  The push plate helps to protect the door of physical damage that could be caused by a hand or arm coming in contact with the door while pushing the door open.
        The pull plate is normally the same push plate with a handle added in order to pull the door open. These plates also act as a decorative piece of hardware.
        You may normally see these  used on doors that can swing in both directions , like a door going into a kitchen of a restaurant.