That detail is implementation dependent. The site that wants to push to your browser hits up a third party push service provider that the user uses to get push

That detail is implementation dependent. The site that wants to push to your browser hits up a third party push service provider that the user uses to get push notifications. That will probably Apple for iOS and Safari, Google for Chrome and Android, and I'm guessing Mozilla might provide one, as well as a host of other smaller companies that might be interested.