Trent 800
I'll stick my hand into the fire for this one, but as usual do your own research to find out if my post is accurate or not. If not, please feel free to correct!
So here we have some information:
B777-200 - Trent 877/875
B777-300 - Trent 884B/892/895
All these engines should essentially be the same engine, but were each "tailored" to the specifications and requirements of each individual airline. So if the Cathay FCOM states that -200 and -300 uses 877 and 884B, it simply means that the original Trent 800 was modified especially for use with that particular CX aircraft model. I am not too sure how this is done, but one way I can imagine would be to re-program some computer components in the ECU to produce an optimum amount of thrust. This is similar to an engine-derate process, as far as my understanding goes.
Hope this helps, or at least does not create further misunderstanding.