For Windows RT, we have windowsrt, a tag which existed but had no questions in it until I just asked one (a number of "Windows RT" questions need tagging with it). No tag synonyms. I request that it be renamed to windows-rt. (I would have used that, but because windowsrt existed—in spite of having no questions—it forbade my creating windows-rt.)
For Windows Runtime (WinRT), we have winrt. A well used tag. No tag synonyms. I suggest that it be renamed to windows-runtime, with winrt retained as a synonym. Alternately, it could remain winrt with windows-runtime added as a synonym. There has already been discussion about which the tag should be, with consensus at that time (a year ago) being in favour of winrt, but since Windows RT has come on the scene (I don't remember whether it had been announced at that time or whether it was called Windows on ARM, but I don't believe it was yet Windows RT) it might be worth re-evaluating that decision as the potential for confusion is higher. (Though too, the name "WinRT" is probably more firmly cemented as what people understand.)
Naturally, the tag wikis need to make the distinction clear.
Quite why Microsoft chose to do it this way, I don't know. But they have, so we need to make the best of it and attempt to minimise tagging problems.