Windows Phone 7, Windows Phone 8 & Windows Phone 8.1 (Targeting Silverlight) uses Silverlight API's. And how Windows Phone 8 & Windows Phone 8.1 relate to Silverlight, well they use the Silverlight API's that are available for mobile application framework.
Windows 8 & Windows 8.1 both target WinRT API's. Currently Windows Phone 8.1 also support WinRT API's. So, if you want to create Windows 8.1 & Windows Phone 8.1 applications that you can do by creating a Universal application targeting both the platforms (They have convergence of 90%).
You can develop Windows 8, Windows 8.1, Windows Phone 7, Windows Phone 8 & Windows Phone 8.1 applications using C# & XAML.