The first thing to understand is that notifications aren't specific to either the iPhone or the Apple Watch. They're the same old notifications we've been dealing with for years, and nothing has changed. That means that there's no such thing as an "Apple Watch-specific notification" or an "iPhone-only notification." iOS decides where to route a notification based on its own heuristics. There is no way to programmatically control which device receives an alert.
That said, stk is correct that you will have to add actions to a category that you set for your notification. The Notification Essentials section of the Apple Watch Programming Guide has some sample code.
Because there is no such thing as an iPhone- or Watch-specific notification, you're correct that you will see these actions on both devices. So, you'll have to do something meaningful on both platforms. This makes sense, because iOS decides where to send the notification, so it should be handled appropriately wherever it's sent.
"WatchKit Simulator Actions"
in yourPushNotificationPayload.apns
...??? – M Zubair ShamshadExample 5
– M Zubair Shamshad