First off, they have different genera and bloom at different times. Most plants sold in the trade under the label "Christmas Cactus" are Thanksgiving Cactus. Thanksgiving Cactus has the most notched leaves, followed by Christmas Cactus and then Easter Cactus. On to the flowers. An Easter Cactus plant has star-shaped blooms, whereas a Christmas Cactus has larger, shrimp-like flowers. Both of these holiday plants are tropical epiphytic cacti, not desert cacti. And, from what I've seen, Christmas Cactus plants ultimately get larger than Easter Cactus plants.