Just wondering how that is handled, like if they just give you another copy that you can gift to someone or something. I want to buy the 2K pack but I already have Borderlands. Being able to gift it to a friend would be awesome though, because I don't have many people to play with right now.

You can gift them

I can't remember what I did this for recently but when I bought another copy they told me I wouldn't be able to do this. Is it different for different games?

It depends on the game. You are just out of luck for most of them, but some will allow you to gift the extra copy. Not many allow this though, so don't count on it. For example, during the Black Friday sale I bought a back that included Flotilla, but I already owned it. In that case I did not get another copy to gift.

You can gift extra copies in a few specific cases. Steam's knowledge base has the details:
 

Extra copies will only be issued as a special promotion in the following cases:

1. Users who own "Left 4 Dead" and then go on to purchase "Left 4 Dead + Left 4 Dead 2 Bundle" will receive an extra copy of "Left 4 Dead"
2. Users who own “Half-Life 2” and go on to purchase “The Orange Box” or the "Valve Complete Pack" will receive an extra copy of “Half-Life 2”.
3. Users who own “Half-Life 2: Episode One” and then go on to purchase the "Half-Life 2: Episode Pack”, “Valve Complete Pack” or “The Orange Box” will receive an extra copy of “Half-Life 2: Episode One”.
4. Users who own "Dawn of War II" and then go on to purchase "Dawn of War II Gold Edition" will receive an extra copy of "Dawn of War II"
5. Users who own "Titan Quest" and/or "Immortal Throne" and go on to pre-purchase "Darksiders" will receive an extra copy of "Titan Quest" and/or "Immortal Throne" 
6. Users who purchase the available four packs for specific Steam titles will receive three extra copies of that title to gift to friends.