The best way to tell them apart, other than the time of year that they bloom are the shape of their phylloclades or leaf segments. If the plant has broad, thin leaves that have three points on each side, you are looking at a Thanksgiving cactus.
The Christmas cactus Schlumbergera bridgesii has more scalloped leaveshile. While the Easter cactus Schlumbergera gaertneri are more round with tiny soft bristles on the edges. These bristles are aerial roots which is why in their native environment Brazil rainforests, grow in trees and rocks (epiphytic). See drawing. The time of year that these beauties start to bud are triggered by the day length. So as fall approaches the day light begins to shorten and the darkness is longer thus gives way to the description of a ‘short day’ plant. Optimum conditions for flowering is 8 hours or less of daylight for about 6 weeks and cooler night temperatures in the 50’s.
Relatively easy to care for, they have little to no pest problems. They can be very long lived, over 100 years, that are known to have cuttings passed down from generation to generation. Root rot is most common reason these plants die. Remember they are succulents, that like high humidity, bright but filtered light and well-drained soil. Use containers with plenty of holes to allow good drainage. Fertilize monthly June thru August with a balanced houseplant fertilizer at half-strength. There are a plethora of colors ranging white, salmon, watermelon pink, reds and single double and even triple blooms. What a great holiday gift or any occasion for that matter! Photo credit: Iowa State University Extension & Lisa Strange. More information go to https://extension.umn.edu/houseplants/holiday-cacti