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First, I don't agree that MS Style Guide says this is a page:
Refers to one of a collection of web documents that make up a website. Use page to refer to the page
the user is on, that is, the particular document, or to a specific page such as the home page or start
Also, use page instead of screen to refer to an individual screen within a wizard.
As the original question points out, the "page" (the web "document", or that which has a specific URL) *contains* the application, but the application has a series of different "screens" within it. When you change screens you don't change the URL (the container), and the browser doesn't store these screen changes in its history. I would say these widgets are whatever the application lexicon calls them... Views, tabs, or even screens. But they are NOT pages, and the *browser* lexicon doesn't apply, IMO.
What's interesting here is that the line between application and content is getting hazy. For technical writers this is a good thing. That this question comes up, and that (no matter who's right or wrong, or if there IS a right or wrong) you can argue completely different answers, says that the presentation side of an application is increasingly coming into the content domain... Literally, and not just figuratively.
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