By my definition, a website is a [usually] publically accessible site that reflects fairly static data and doesn't provide for much in the way of functionality (it doesn't DO anything, it just displays information).
A web application if often for an Intranet (but can easily be public), is usually very dynamic, and is based around one or more functions (it DOES stuff).
These days, the lines are quite blurry. For example, many corporate websites are filled with very dynamic information and web applications (like press releases, job application forms, etc).
The reason that it matters, is that the design of your site or application should be driven by the purpose, and the purpose of a website is usually quite different from that of a web application.
Here is an article I found online that seems to agree.
Think about the Web sites you visit. What do you find there? Content. You see lots of text, graphics, color, animation, and sometimes even glitz and gimmicks, right? Most Web sites are designed to encourage browsing, searching, and exploration.
Now think about the applications you use. You use them to complete tasks. Rarely do you see exciting graphics ... Rarely do you browse, search, or read lots of text. You are a fairly captive audience and don’t need glitz or fascinating content to keep you there. What you do need are quick and easy methods to complete your tasks.