After the Americas became accessible to Europeans there was a brisk exchange of bean types, although details are a little hazy as to which type of bean originated where. The exchange benefited both continents and bean species proliferated.
Today there are around 18,000 legume species, not all of them edible. A complete category of all bean types is impossible; beans are notorious for being genetically variable. A bean plant grown from seed can produce offspring whose beans bear little resemblance to the parent bean.