App push notification is a message that pops up on a mobile device. App publishers can send them at any time; users don't have to be in the app or using their devices to receive them.
Web push notifications are messages that come from a website. You get them on your desktop or device even when the concerned web page is not open in your browser. They are a brand new/ nascent marketing channel to re-engage your visitors without knowing their email or other contact details.
