You have two basic types of cheaters in COD, or overall really.
The Cheater-Griefer is out to specifically ruin everyone else's fun. That becomes the game, the actual game is the means to an end. This person is a depraved loser. Other forms of non-cheater Griefing may include (but are not limited to), blocking a route such as a bridge or a door, and not moving. Mobbing up on low level characters in PVP, and/or robbing them of their lowliest game possessions to make more difficult their noobly situation. Or almost any other way to not "play right". The second type of griefing can be really hilarious if done right (assuming you're not the victim, though sometimes even that can be funny).
Also there is the Booster-Cheater, the meta-game (leveling up to an arbitrary number, or getting a higher prestige level) whore. This person is even lowlier than the Cheater-Griefer because at least they have a humorous goal in mind, even if they are total dicks about it. The Booster-Cheater actually assigns value to the in-game rewards, and works dilligently to chase that goal, as opposed to actually having fun playing the intended game. Hilariously this person often loses interest in the game after reaching said pointless goal.