^ Phew, I hope I can give you a proper answer, that sure was alot of text and I hope I got you right...
So yeah, you were right with your statement: If you buy a Steamworks game (a retail game that makes use of the Steam service) or buy a game online via the Steam Store, it is permanently tied to your Steam account and added to your games list. Steam doesn't tie your account / games to IP's nor to hardware setups and there is no such thing as an installation limit (at least not from Steam itself, but in a case like CoD there is, since they decided to add the Solidshield DRM).
So, how does Steam work? If you don't have a Steam account nor Steam installed and you buy a retail game that makes use of it, things work like this:
1.) Before the installation of the game, Steam is installed on your HD.
2.) You are able to create a Steam account then. If you already have one, you can log into it right then.
3.) You are asked to enter the product key that comes with the game. Once it is entered, the game is tied to your account. The product key can be only used once, so you can't use it again on another account.
4.) The game is installed from the CD / DVD. If you want to use your disk as a frisbee instead, you can also download the game via Steam (comes handy if you should lose your disk or in case it should get demaged).
5.) Once the game is installed, you can play it. You don't even need to insert a disk into your drive anymore.
If you want to install the game on another computer, just download the Steam installer from the official homepage or just do the same as already above and do it via disk. Log on into your account, click on the game in your library and hit the "install" button just as before. Some EULA's however "prohibit" installing the same game on multiple computers at once, though.
So, what Steam actually does is following: You can only play online with a single account from a single computer at once. Which means, you can't go online with the same account on two different computers simultaneously. And that's basically how the Steam DRM works.
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