Is there any difference between using the same chain ID (Chain I, atloc P and Q, half occupancy) or using the different chain ID (Chain I, atloc P, half occupancy and then Chain K, atloc Q, half occupancy)?

This is addressed in the documentation:

http://phenix-online.org/documentation/reference/refinement.html#occupancy-refinement

as well as here:

"13 typical occupancy refinement scenarios and available options in phenix.refine"
http://phenix-online.org/newsletter/

Pavel