Difference between WinRT and Windows RT - Confused?
Though both these seems similar and confusing, but actually they aren't.
WinRT or Windows Runtime
As I posted earlier, it is a new set of API's built on Windows8 kernel to develop Metro style applications.
Windows RT (originally also known as Windows on ARM)
It is a version of Windows8 operating system for ARM architecture and instruction sets. Seeing the popularity and huge number of devices powered by ARM processors in market, Microsoft targeted application development for ARM devices as well. Windows RT would be pre-installed in the ARM based devices and would have touch optimised versions for Microsoft Office suite.
Apps built on Win32 API can't be used on ARM architecture and thats apparently the reason why WindowsRT(WOA) doesn't have Windows Media Player in it.
WinRT(purely) must be used to build apps/softwares to run on Windows RT.