Twitter is not just a website, it is also a platform that facilitates push notifications so that people can receive information in near real time, passively, no need to visit a website. So neither Twitter or a website alone is the answer.
But that is not entirely accurate. The website/app instance is running on the phone/device/whatever. It is not passive. The user opened it ( or opted to keep it open in background ).
In other words, 'website' is visited. Information is accessed and sent back to the requester.
> The website/app instance is running on the phone/device/whatever. It is not passive. The user opened it ( or opted to keep it open in background ).
That's not how it works. Unless it's the foreground application, the application is not running; it's not kept open in the background. Instead, what happens is that the application registers with a push notification system when the user first opens it and logs in. When the user should be notified, the website sends a message to the push notification system's central servers, which notifies the phone (the push notification system does stay open in the background, but it's shared by all applications in the phone), which then starts the application on the phone to show the notification.
A user gets notifications without having to look at their phone. That seems passive? Sure, prior installation & configuration of the app days/months/years beforehand was an active step but once you give it permission to send you notifications all of those notifications are received without user intervention required.
It is true that on the phone the way the information is presented is through an app ( and we can argue whether it is just a more restricted browser ), but definition of a website is:
related content that is identified by a common domain name and published on at least one web server
If that is the case, app is just a bastardized website.