There are a number of different cactus species sold as "Christmas cactus," including Schlumbergera opuntioides, Schlumbergera kautskyi, and Schlumbergera microsphaerica.
Schlumbergera opuntioides | Schlumbergera microsphaerica | Schlumbergera kautskyi | Schlumbergera | ''Schlumbergera'': Taxonomy | Close-up of a ''Schlumbergera |