Paul and thenerve are correct. They are all members of the genus Lampropeltis. They are also all technically Kingsnakes, which was a generic common name applied because they are ophiophagous, meaning they will eat other snakes. The King Cobra got his common name the same way (the scientific name Ophiophagus hannah also obviously comes from his habit of eating other snakes).
The Kingsnakes are subdivided into two separate groups (genera) both by taxonomy and (mostly) common names, the Milk Snakes and the Kingsnakes. For the most part Lampropeltis getula are the common Kingsnake and it's variants and Lampropeltis triangulum are the Milk Snakes. It would be nice if the division was clear, but it's really not. There is some crossover use of common names between the groups, such as the Scarlet King Snake Lampropeltis triangulum elapsoides, a snake with a King Snake common name and Milk Snake taxonomy. Most of the Milk Snakes are tri-colored and most of the King Snakes are not. The King Snakes are usually black or brown with white or yellow bands, stripes or speckles. One (of a few) groups that throw a wrench into the idea of clarity here are the Mountain Kingsnakes, Lampropeltis pyromelana and Lampropeltis zonata. They are tricolored and by common name, King Snakes.
The truth is that there are several different "types" of King Snakes. There are the Common Kingsnakes, the Milk Snakes, the Mountain King Snakes, the Mole King Snakes L. calligaster, the Gray Banded Kingsnake and it's variants L.mexicana, and Ruthven's King Snake L. ruthveni.