Zygocactus and Schlumbergera are one and the same. It really depends on where the plant came from. Some people still call them Zygocactus and others call them Schlumbergera. I am sure you know that, I am sorry if I am repeating something already known.
One of my reference articles from The Cactus Collection states, "The word Zygocactus is often used to refer to this plant, but merely describes the manner in which the joints are connected and is of no taxonomical importance. Zygocactus are actually Schlumbergera hybrids (correct botanical name) between Schlumbergera truncatus and Schlumbergera bridgesli, and are also known as Schlumbergera x buckleyii" NOW ARE YOU REALLY CONFUSED?
Have a good evening. I am going to bed.
