In a document-oriented switcher, the icon is the application, while the window is an open document (for a relaxed definition of 'document' when speaking about a terminal).

So clicking on the application icon will present the user with all documents opened by this application, hence will raise all of its windows, while modifier+clicking will create a new document.

That sounds to me like an application oriented switcher. The application is focused, not the document.

This has really annoying consequences in OS X where it trips me up all the time. For example, I open a pdf from within Safari. I finish reading and close it. I expect to be back in Safari: I'm not; I'm focused instead on a completely unrelated photograph that I'd opened ages ago and forgotten about.

Linux GUIs were traditionally all about documents. As they've tried to converge with Mac and Windows, they've become more about apps. IMO that's a shame, but there it is.

Like others have said, it's more about what the icon represents. A window (maybe a document) or an application. I prefer the application metaphor more than the window metaphor. I've come to like this since I don't always need to see all my windows to access a running application.

That said, there is plenty of other questioning that can arise like, does one close the application when all windows are gone? Tricky.