The servers for multiplayer FPS games on the PC are usually owned (rented) by players themselves from a game hosting company. The vast majority are setup to be public (pubs), and anyone can connect and play for free.
For console games however, usually either the console manufacturer uses their own server farms, or the game is designed to be hosted on one of the players console machines and he will be the host. Depending on the console/game this will either be free or incur a yearly charge of something like 50 bucks or whatever.
And no, console and PC players do not (and cannot) connect to the same server.exe, not only in cod but most multiplayer games.
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