There are 3 types of remarkably similar cacti called Christmas cactus, Thanksgiving cactus, and Easter cactus. What separates them are the blooming times.
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The Christmas and Thanksgiving cacti need around 6 weeks of short days to initiate blooming. The Easter cacti need 8 to 12 weeks of short days required for blooming.
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There is a difference in their leaves also. The Thanksgiving cactus (Schlumbergera truncate) have claw-shaped segments and the Christmas cactus (Schlumbergera bridgesii) have rounded segments.
The flowers are different on the Easter cactus (Hatiora gaertneri) are larger and daisy-like.
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If your plants are dropping buds, I can be due moving the plant to another location changing light conditions. The plant due best being root-bound. If the plants turn reddish, the problem is usually too much sun or lack of water (do not overwater, have good drainage).
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