No, I wasn't confused, but thanks for that. Zygocatus is the former genus name for what we now call 'true Christmas cactus, Schlumbergera x buckleyi. The irony is putting this long-abandoned name/label on Thanksgiving cacti, Schlumbergera truncata.
Paul Brunelle, a highly respected cacti and succulent horticulturist, states:
"The true "Christmas Cactus" is Schlumbergera x buckleyi, a hybrid between S. russelliana and S. truncata produced in the late 1840s by William Buckley at the Rollisson Nurseries in England. There are possibly two, perhaps three slightly different surviving clones (vegetative descendants created through layering or cuttings) of three hybrids of this cross, named S. x buckleyi 'Buckleyi ' , S. x buckleyi 'Rollissonii', and possibly S. x buckley 'Snowii'. 'Rollissonii', has flowers magenta in colour, 'Buckleyi', with white tube shading to magenta petals, and 'Snowii', with smaller magenta flowers and stem segments. The name Schlumbergera bridgesii, still seen occasionally, was mistakenly published for it very early, and only in 1964 was the plant's proper history and correct designation traced and reestablished by Will Tjaden, a member of the Epiphytic Plant Study Group in England.[1]