If you want to use the free version of Visual Studio for Windows Phone, then you have to use the 2012 (Windows Phone 8.0) version which you can download here…
http://www.microsoft.com/en-us/download/details.aspx?id=35471
Alternatively, you can use the Pro 2013 version (not free) which supports both and more.
If you want to know the details why, the Windows Phone 8.1 SDK is used to build WinRT XAML based applications, which does not support Windows Phone 8.0 devices. The Windows Phone 8.0 SDK is used to build Silverlight based XAML applications, which supports Windows Phone 8.0 and 8.1 devices. They use totally different UI frameworks. The Windows Phone 8.0 market is still the dominant one right now, so it makes sense to continue to target this SDK. The disadvantage of using this SDK is that your apps won’t run on Windows tablets (ie: Windows RT) or on Windows 8’s metro interface, because those platforms only support WinRT XAML based apps. (Microsoft didn’t add universal app support until recently.)