Someone probably move the post for you.
Push Notifications and the “bubble” on app icons are two different ways to notify the user. I did see your Feature Request for the “bubble” and I think its a good one.
Push Notifications are the messages the present on the lock screen or if the phone is unlocked within the banner or over the app. These can be created using the Notify step in a Workflow. the message is custom and you can even include links to a focused area of the app such that when a user taps it they are taken directly to that app area.