Movie screen. TV screen. Desktop screen. Laptop screen. Tablet screen. Smartphone screen. Wristwatch screen.
Post PC Or PC Plus
Screen size is the primary way to classify, really. Each screen could come with a keyboard. A virtual keyboard is as good as a physical one. And there is no limit to how much intelligence you can add to any particular screen. (Supercomputing + Neuroscience + Nanotechnology, Adding Intelligence To The Biggest Screen: TV)
Imagine a scenario where there is ubiquitous, wireless, global one gigabit per second broadband. We as humanity basically live in this sea called the Internet. That is the first country anyone belongs to. (Tim Berners-Lee: The Internet Is Not A Country)
In such a reality the browser is your interface on all screens. And it likely would be build for one, build for all. This is post HTML5 reality you are talking about. (HTML 5 And The Small Screen)
Right now much of the buzz is with the smartphone. And for now looks like the smartphone is moving to become the center of the known universe. It is one screen that you can have with you, always, and is big enough.
But then this seven screen classification sits on the premise of 2D computing. 3D computing has huge implications.