For me the biggest difference is the relationship between the pages. In a website project, each page is essentially its only little project which is, or can be, compiled separately from the rest of the pages in the application.
In a web application, the entire project is essentially compiled into a single DLL, very much akin to a class library project.
Some other differences:
- You can do live edits of web sites project on a deployed server. Open up the file, make an edit, and the next time the page is visited it will be re-compiled. Some people may consider this a bad thing.
- A website has no project file (e.g. .csproj), which can make persisting settings with a project challenging.