On your side of the pond, the best book for pictoral anatomy of a double, construction process, and terminology of the parts would be "Lock, Stock, and Barrel" by Cyril Adams & Robert Braden (Safari Press, ISBN 1-57157-020-9). Its about SxS shotguns, but will meet your needs well.

There is also a good internet site or two, other posters will no-doubt have a few suggestions here. The Internet Gun Club and Galazan are two oft-quoted sites for history and nomenclature.

There will always be problems with British versus American terminology for double guns. You guys use the term "water-table" for the action flats (Huh? Water causes rust! Should be kept away from fine guns!), "barrel lugs" for lumps, "forend lug" for the loop, "internal hammers" for the tumblers, etc. In Australia, our double-gun heritage is British, but our shooting influences post-WWII are straight American. Plenty of scope for confusion here!