According to Windows Phone API reference there are 11,000 Windows Runtime API members supported on Windows 8. The phone supports a subset of 2,800. The Phone also has 600 members not supported on Windows 8.
Search for "Windows Store Apps" "Windows Phone 8" "API is not implemented" to see some examples.
Windows Phone 8 and Windows 8 platform comparison shows the libraries supported in the Common native API: DirectX 11.1, XAudio2, MediaEngine, STL, CRT, and WinSock.