WinRT / Windows Runtime is a software layer that sits on top of the OS, for devices using processors based on the ARM architecture and instruction set and that is at the base of the new Metro design language approach. It’s primarily a set of APIs to build Metro apps for all Metro-supported platforms (including for Windows 8 for ARM).
Windows RT / Windows 8 for ARM
Windows RT (where RT also means “runtime”, to make things as confused as possible), used to be known as Windows 8 for ARM. It is a version targeting hardware manufacturers (mostly aiming at the tablet market).
Windows RT is the newest member of the Windows family – also known as Windows on ARM or WOA. This single edition will only be available pre-installed on PCs and tablets powered by ARM processors and will help enable new thin and lightweight form factors with impressive battery life. Windows RT will include touch-optimized desktop versions of the new Microsoft Word, Excel, PowerPoint, and OneNote. For new apps, the focus for Windows RT is development on the new Windows runtime, or WinRT, which we unveiled in the forms the foundation of a new generation of cloud-enabled, touch-enabled, web-connected apps of all kinds.