Yes there are several clubs in the United States but the two you asked for is what i addressed. You have to pay a membership fee if you want to be in this group. Some others are not as big but are open to most and free to belong.
They are the same group. "BREEDERS" was removed from the name to better serve all persons who are interested in the sussex chicken breed. It was felt you did not have to breed or show sussex to be in the association when it was changed. This gave those who just had a few backyard sussex...