I'm a little confused. Do the Libertys have a different set of serial numbers than just the 2Bs?

All King horns are on the same serial number list. The Liberty originally referred to a single bore (0.481", I think). There is the Liberty 2B which is dual bore, which eventually was called 2B, then 2102, and then 2B again. There is a single bore called the Jiggs (after Jiggs Whigham) that is 0.491" (I think).