Creating a "Website" in Visual Studio uses ASP.Net WebForms, using a method that means the pages are compiled on-the-fly - there's no DLLs created. This method is not really encouraged, and is no longer the default in Visual Studio 2010.
Creating a "Web App" in Visual Studio also uses ASP.Net WebForms, but compiles the site, so the code-behind and any class files are compiled into a DLL.
MVC is an alternative framework to WebForms that also uses ASP.Net.
As for the Web Client Software Factory, this is a toolkit to help you create a Web App project in a "patterns and practices" way. I've only just looked at the site, but it seems to be using WebForms as opposed to MVC.
So there's essentially a choice between WebForms and MVC in terms of ASP.Net frameworks, but after making that choice, there's several other sub-paths you can go down.