And not just because it's blooming now, just in time for Thanksgiving. There are many different types of this cactus. Thanksgiving cactus has flat leaves with serrated edges, and the flower looks like a bird in flight. Christmas cactus has smoother-edged leaves and they tend to spill over the edge of a planter, like a vine. The flowers are more like full, layered trumpets. Thanksgiving cactus above. Christmas cactus below. See the differences?