Many people have holiday cactuses in their homes or gardens and with a bit of research and help from people on FB gardening groups I have finally understood the differences between the 3 most common.
To make matters worse, nurseries or garden centres often just call them holiday cactuses without saying which holiday cactus it is: Christmas (Schlumbergera buckleyi - mistakenly labelled previously as schlumbergera bridgesii), Thanksgiving (Schlumbergera truncata) or Easter (Schlumbergera gaertneri (formerly known as Hatiora gaertneri). The latter is also known as rhipsalidopsis gaertneri.
To confuse the issue even further, these holiday names originate from the Northern hemisphere, so, a Christmas cactus (Winter time in the Northern hemisphere) does not flower at Christmas time in the Southern hemisphere and flowers in June/July (our Winter)as does the Thanksgiving cactus whilst the Easter cactus in the Southern hemisphere flowers in Oct/Nov (late Spring). Seasonal names rather than holiday names would, therefore, be more accurate appellations.
These cacti are also epiphytic, so, just like orchids - they grow on other plants in the wild. This does not mean that they cannot be planted into soil. As you can see from the photos below, mine are all planted in soil. I have found that they prefer indirect light as, here in South Africa, the sun is just too hot in Summer. I have some outside as well as ones inside. As these cactuses originate from tropical rainforests in South America where there is lots of humidity, they do need more watering than a true cactus and they are very similar to epiphyllums in that regard. Interestingly enough, schlumbergeras were previously called epiphyllums(also known as orchid cacti).
So, how does one tell holiday cactuses apart? The Easter cactus is very easy to differentiate. As can be seen from the photo below, the flowers are pointy and look like stars. This cactus also blooms only once per year whereas the other two bloom twice in succession.
The other two types of schlumbergera are differentiated by means of their leaves, anthers and flowers.
The Thanksgiving cactus (Schlumbergera truncata) has distinctly spiked edges that almost look like little horns. There can be only 2 or sometimes 4 "horns". Its anthers are yellow. It is this cactus that gave rise to the Christmas cactus, in other words, the Christmas cactus was bred from the Thanksgiving cactus and is, therefore, a hybrid. The Thanksgiving cactus is also the only cactus that can be called a zygocactus.
Then there is the Christmas cactus (Schlumbergera buckleyi) that has scalloped edges and its anthers are a purplish, pinkish colour and it has white stamens.
As you can see, the Christmas cactus also has a different-looking flower where one can see the stamens hanging down with petals that seem to have been peeled back like a banana, It likes direct sunlight, but as mentioned, before, it needs to be moved out of a burning midday summer sun. This cactus will bloom when there are cool night temperatures ranging between 10-13°C, but if the temperature is higher, it needs uninterrupted darkness ranging between 13-15hours. You can create this darkness by covering it with a black plastic bag.
Epiphyllums, however, have much larger leaves and flowers, but one can see distinct similarities.
Above is the epihyllum crenatum or epiphyllum oxypetalum (not sure which it is) and, unfortunately, I do not know the name of the red one below, but it is possibly epiphyllum ackermannii (red orchid cactus or the lady finger cactus). It is different to oxypetalum which has flat leaves(clades) where the red one has a triangular-shaped leaf. I have come to realise that correctly identifying a plant is not very easy and can be very confusing, so my attempts above are exactly that - just attempts.
Disclaimer: I am no expert and am just trying, for my own interest and knowledge, to clear up some confusion when it comes to these beautiful plants. If anyone can correct me, please chat with me.