Setting
in Web.config seems to do things that you can also set in Visual Studio in Project properties, Build tab. Are they
Set compilation debug="true" to insert debugging symbols into the compiled page. Because this affects performance, set this value to true only during development.
They are not connected. The compilation tag is ASP.NET only, while the project option one is for Windows Forms, console, WPF and so on.
ASP.NET compilation is so special, so you have to dive further to learn about every piece of it,
http://msdn.microsoft.com/en-us/library/ms178466.aspx