I got an R4 DSHC (WWW.R4I-DSHC.COM) from a friend who recently returned from Thailand. When I got it it had some odd firmware on it. It booted up and displayed an R4 menu, where I could choose to go to games or moonshell at the startup screen. The Games option booted up YSMenu, still with all the R4 paraphernalia. I was happy for the first day, then I tried putting a skin on, not realising anything about it and thinking it was your average R4. Needless to say, nothing worked, and eventually I saw a Youtube video of an R4 and realised that I was supposed to have three options at startup. Thanks to Wikipedia, I found out the microSD face I saw when I booted up was a TTDS thing, so on a whim I wiped the card and installed TTDS firmware using a tutorial here. Surprisingly, it worked without a hitch. I also decided to install YSMenu, which clued me in to my old firmware's true nature. I then installed Moonshell with YSMenu support.
TL;DR R4 DSHC is actually a clone of TTDS with a modified version of YSMenu as firmware and can run normal DSTT firmware fine.
TL;DR R4 DSHC is actually a clone of TTDS with a modified version of YSMenu as firmware and can run normal DSTT firmware fine.