WPNS is the similar service for Windows Phone applications. WNS is specifically for Windows 8 metro style applications.
WNS pushes Toasts, Tiles and Badges. The best example of toasts is Skype toast indicating an incoming call. The best example of tiles is Weather showing current conditions. The best example of badges is Email showing your unread count. Each of these allows you to deliver value to users. None of these require your application to be running.