Archbar was the earliest, used widely in the 1800s, but banned from interchange in the early 1900s (1920s?).
Barber and Bettendorf are actually brand names, and usually refer to cast frame trucks, in multiple variations, both of frame appearance and spring combinations. These became common in the early 1900s, with solid bearings, and are still used today, with roller bearings. I'm not sure about Bettendorf, but as far as I know Barber is still in business.
In both cases, they were used under any and all types of freight equipment, cabooses, and steam tenders, although as far as I know there were no 6-wheel archbar trucks.