>Or, in my own words, ignore Push notifications and just use WebSockets.

Battery consumption is a big difference between the two. To keep the connection open, you need constant connection with the radio hardware, keeping it running, having it actively reconnect etc. Push notifications don't need a continous connection, the provider just connects from time to time and delivers the notifications then. There's some latency involved, but the power consumption is orders of magnitude lower.

The key difference is that push notification's backing "service" are out of band with the subscribers.

Applications can subscribe to push notifications and get them even if they're off (the OS runs them and gives them the notification). WebSockets are closed if the app closes.

A little to your point, the backing notification service might rely on WebSockets or polling, or a mixture of both, in implementation.

Push notifications are for popping a toast on the user’s device, like a new text message notification.

> Or, in my own words, ignore Push notifications and just use WebSockets.

I wonder whether all the people who blindly accept utter nonsense ChatGPT tells them were applying any critical thinking before the age of AI.