What’s the difference between notifications and push notifications? You can boil down the difference to be a matter of where the notification is coming from.
Regular notifications (internal)
Regular notifications are messages created internally by an app installed on your device. For example, if you’re on a free trial with an app, you’ll usually get a notification when the trial period is running out. Other common internal notifications are reminders, updates, and news related to the app.
Push notifications (external)
Push notifications are messages sent from external sources outside of the device you’re using. A good example is a chat app. If someone messages you on Twitter or Instagram, you will get a push notification on your device (unless you disable push notifications in your app settings).
If you’re playing on your console (Playstation, Xbox, Switch) and someone invites you to join an online game, that’s a push notification.