When I read Apple Docs, they mention 3 types of notification: local, remote, and silent.
Local notification can be inferred from its name, that is sent by the app loc
Silent push notification reaches device, user does not know anything about the notification but his app gets the notification and app will be given some time to download new content and present it to the user, regardless to the state of the app (i.e. running or not running)
Remote push notification method is called only when your app is running. If app is suspended or not running, then the system wakes up or launches your app and puts it into the background running state before calling the method. This method is intended for showing the updated content to the user.When this method is called, your app has up to 30 seconds of wall-clock time to perform the download operation and call the specified completion handler block. If the handler is not called in time, your app will be suspended.
For more technical details, you can go through this links:
Apple Notifications
Silent Notifications