Is there a difference between Tyrant gear other than just the name?

Oh, derp. Didn't know they were class specific. Still good to know. So you said it's possible to transpose to a Sweetwater? Guess that's one way to make the cape class-wide so I only need one cape for all classes in a sense.

If you're planning on sharing them, you'd probably want 5 tyrant items since otherwise, you'd need one Sweetwater (and a corresponding Tyrant) for every single character as they're completely untradeable once worn or transposed (with the exception of like, once if the scissored status can still be transposed). It kind of makes it being common class pointless, other than making it so you don't have to find a specific one.