The Wizard, your first link shows WHO and not WHAT.
I think orca was a bit tongue in chief. I also think the real answer is that one it the political head and the other the operational one.
Sir Stephen is on the board whereas CINC Air is not
Air Force Board - Wikipedia, the free encyclopedia
Interestingly CINC Fleet is on the Admiralty Board
Admiralty Board (United Kingdom) - Wikipedia, the free encyclopedia