What's the difference between a web site and a web application?

This is totally personal and subjective, but I'd say that a website is defined by its content, while a web application is defined by its interaction with the user. That is, a website can plausibly consist of a static content repository that's dealt out to all visitors, while a web application depends on interaction and requires programmatic user input and data processing.

For example, a news site would be a "website", but a spreadsheet or a collaborative calendar would be web "applications". The news site shows essentially the same information to all visitors, while the calendar processes individual data.

Practically, most websites with quickly changing content will also rely on a sophisticated programmatic (and/or database) backend, but at least in principle they're only defined by their output. The web application on the other hand is essentially a program that runs remotely, and it depends fundamentally on a processing and a data storage backend.

Websites are primarily informational. In this sense, http://cnn.com and http://php.net are websites, not web applications.

Web applications primarily allow the user to perform actions. Google Analytics, gmail, and jslint are web applications.

They are not entirely exclusive. A university website likely gives information such as location, tuition rates, programs available, etc; it will likely have web applications that allow teachers to manage grades and course materials, applications for students to register for and withdraw from courses, etc.

You can charge the customer more if you claim it's a web application :)

Seriously, the line is fine. Historically, web apps were the ones with code and/or scripts (in Perl/CGI, PHP, ASP, etc.) on the server, and sites were the ones with static pages. Currently, everyone and their uncle's cat are running forums, guestbooks, CMS - that's all server code.

Another distinction is along the subject matter lines. If it's a line-of-business solution, then it's an app. If it's consumer oriented - they call it a site. Although technology-wise, it's more or less the same.