Is the Director’s Cut the only PC version of "The Chronicles of Riddick: Escape from Butcher Bay"?

A few years ago, I got a copy of The Chronicles of Riddick: Escape from Butcher Bay for Windows. Recently, I heard of a director’s cut of the game. I have found photos of the cover/disc including some that say director’s cut, some that say developer’s cut, and some that don’t say either.

I cannot find any information on what (if anything) is different (for the PC versions, not from the Xbox release). In fact, the research I have done seems to indicate that the director’s cut is the Windows version. That is, the game was originally for Xbox, then the Windows port was dubbed “director’s cut”.

Is this the case?

Yes, the PC version of the game is the Director's Cut. The differences are covered in this review, in the second paragraph:

Its visuals have been enhanced to be proportionally outstanding even when measured against the PC's extremely high standards; its controls have been optimized to make it easy to pick up by anyone who has played a PC first-person shooter lately; it features a new and exciting gameplay sequence that has been seamlessly integrated into the middle of the story; and it boasts an unlockable "commentary" mode, which annotates the entire game with extensive, often fascinating DVD-style audio commentary from the frightfully talented development team at Stockholm-based Starbreeze Studios.