Yes, a Schlumbergera is the proper name for a Christmas Cactus. These plants can go by other names as well, Thanksgiving Cactus, Holiday Cactus, and Easter Cactus. When searching for the Christmas Cactus at your local greenhouse, you may find them going by the other names. While they are similar their all slightly different the most significant difference is their blooming seasons. For example, Easter Cactus usually bloom closer to Spring, and Christmas Cacti bloom close to Christmas.