When a game says it is multiplayer it means more than one person can play it at the same time. This may or may not mean that it works with Xbox live (i.e. you can play with other people on Xbox live). Multiplayer could also mean that you play on a split screen (using the same console), or via system link.
All xbox games that have the Xbox Live logo on them should work for online multiplayer(i.e. Xbox live). Call of duty 4 definitely can be played on Xbox live. I am not sure if there is a way to play call of duty 4 with each other on Xbox live using the same console. Hopefully somebody else can answer that for you.
If you have friends on Xbox live I know you can set up games so that you and your friends play together and other people on xbox live can join as well. I have done that with Halo 3 several times.