- WinRT (Windows Runtime, unlikely to be what you meant) is a software layer on top of which Metro apps are built, while Windows 8 is the whole operating system;
- Windows RT (most likely the one you meant), this is a version of Windows 8 for devices using processors based on the ARM achitecture and instruction set.
You got the names a bit mixed up apparently - granted they made them confusingly similar - so I just addressed both and edited your question accordingly.
WinRT / Windows Runtime
WinRT a software layer that sits on top of the OS, 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).
See the image below for a general approximation of the Windows 8 Platform:
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).
See this post Announcing the Windows 8 Editions of the Windows Team's Blogging Windows blog (emphasis mine):
Windows RT is the newest member of the Windows family – also known as Windows on ARM or WOA, as we’ve referred to it previously. 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 September and forms the foundation of a new generation of cloud-enabled, touch-enabled, web-connected apps of all kinds.
See the original post for a table listing the major differences between the versions, or Wikipedia's Windows 8 Editions article for more details and sources.
Note that only software written using Win RT (the APIs) can run on Windows RT (the OS version).