The Christmas cactus, Schlumbergera bridgesii, blooms later and has smooth stem segments that are smaller and scalloped along the edges. Its growth habit tends to be more pendulous or drooping.
The Thanks giving cactus, Schlumbergera truncata sometimes known as Zygocactus, or claw cactus blooms several weeks before the Christmas cactus. It has stem segments with strongly toothed or pointed edges that make them appear claw like. This cactus also appears to grow a little more upright.