On "British" versus "U.S." usage, I want to point out that supposed differences are often very "soft." Most of the time, the supposedly "British" usage is perfectly natural, common U.S. usage. I think Su.Ki.'s distinctions are accurate and brilliant; I wish I could give more than one thumbs-up. But in real life in the U.S. the words are synonyms, and which word we use depends on what our parents said and which word we've seen more recently.
If we're in an airport and have just paid a "baggage fee" we will talk about "baggage."
If we are in a department store--where, as far as I know, the place where they sell suitcases is always called the "luggage" department--we will talk about "luggage."
I just did a quick reality check at lordandtaylor.com, a good U.S. department store, and if you type "baggage" in the search box it says "No Results for: baggage. We could not find any matches for your search." If you type in "luggage" you get 375 items. "Luggage" is British usage? I don't think so.