As far as I can tell, it is just a fork of MUI. Our MUI4 (I'd say, to avoid confusion, the only MUI4) is version 4.2, copyrighted 2012 by Stefan Stunz. Their is 4.0, copyrighted 2006 Stefan Stunz. I'd also say that the internals of MUI4, which were completely and heavily rewritten, are completely different for this release. As far as I can tell, these are most of the functionalities of MUI4 needed for Odyssey and MPlayer built on top of MUI 3.9.
As often happens, the usual inferior copy of MorphOS functionalities somebody else has to live with...

But feel free to correct me.

Kind regards,
Andrea