I was watching some video tutorial for developing Windows Phone 7 apps (& hoping to develop Windows 8 apps on that basis ;) The guy in the video tutorial was using Visual Studio 2010 and I have Visual Studio 2012. He created a new project using the option "New -> Project -> Silverlight for Windows Phone". Although I don't have such an option I do have an option called "New -> Project -> Windows Phone". This got me wondering whether there is a difference between those two. Could anybody explain the difference between them, if there is any?
Visual Studio 2010 can only make applications for Windows Phone 7. And Silverlight is the only API available to third-party developers on WP7 (even XNA is based on Silverlight).
With Windows Phone 8 (supported by Visual Studio 2012), new kind of applications were added: native (C++ based), HTML5... That's why calling the category "Silverlight for Windows Phone" didn't make sense anymore, and it was renamed simply "Windows Phone".
It's just a name, it makes no difference to you. When creating a new "Windows Phone app" project, Visual Studio will ask you which version you want to target. If you pick "Windows Phone 7.1", you'll get the exact same API that you had in Visual Studio 2010.