There is a general misconception about notifications and Push messages. To explain the difference, we can use the example of SMS.
On your smartphone you might receive an SMS message. Your phone will then notify you that an SMS has been received by displaying this on your lock screen for example. This is not the full SMS message and it is not a Push message either. This is what we call a notification.
You can manage notifications per app on your phone. The SMS app shows you notifications if you wish to. When we send a Push message to your app or the Notifire app, your phone will display a notification that this message has been received and usually shows a part of this message. When you then open the app, the full “Push message content” will be displayed.