... I still see web applications as essentially different from web pages. Much like intranets, they don't have to play nice with other sites or standards (of the non-XHTML kind), because they are closed systems. Their aim is to complete a set task, not to hold linkable, publicly accessible information. When you send an e-mail, do you want its confirmation screen to be recorded in history for public posterity?
I think the essential characteristic defining the divide between an application and a web page is probably this public linkability. If the essence of your project is static information that should be available to a wider community (be it five friends or five continents), then it is most suited to a web page.
Indeed, I'm not sure I see the value of distinguishing between web apps and web pages. In 1992 I used to have the same problem distinguishing "multimedia" from "web stuff". I now realize the issue was one of communities of practice. Multimedia developers and new-fangled web developers were different people using different tools for different markets and different media. But that was a historical accident. They were actually trying to do the same things and acheive the same effects, and they eventually (I think, sort of) converged.
So what does that imply about when to use and not use AJAX? Um, I think that's pretty obvious--if you want non-disruptive time data exchange with the web browser, its the thing to use.
What's not so obvious is knowing what non-disruptive time data exchange with the web browser is good for. But I think we're getting some really interesting ideas...