Here's a good link about WAPs (web application projects) and the differences between WAPs and website projects.
In 2003, your only option (if I recall correctly) was the WAP. 2005 introduced the concept of website projects, where all your code is uploaded to the server and compiled into DLLs on first access. This allows you to easily change your code without having to compile and publish the dlls.
Not a lot of people liked this new way of doing it, so MS created an update to allow for 2003 style WAPs in 2005. 2008 retains both options.
The File->New->Web site option is the only way to create a website application (or, at least it is in 2k8). The only way to create a WAP is to do File->New Project->Web->...