I used to feel like that too, but after kicking it around for a few yrs, it seems like a silly thing to bother being concerned about (except when one may have attached the wrong botanical name to their plant, in which case they probably want to know the difference.) Here's what's going on with my thoughts.
It was apparently difficult to mass-produce the hybrid that is the original "Christmas cactus" because, as is still true to this day, they're not available by the masses, and from what people who have had them around for a while say, they don't re-bloom as readily, profusely, and often well after Christmas. Would they not try to sell us both if they could? I believe so. A plant that can step up to the plate and do what everybody wants more near the time it's expected to happen is the "Thanksgiving cactus," Schlumbergera truncata.
Being a nickname, I see no reason to not sell or label S. truncata as a Christmas cactus. I think a like analogy would be comparing this discussion to a discussion of whether a Schefflera is an umbrella tree or octopus plant. It's both, or neither, or whatever name someone wants to use. Anything but its' botanical epithet is a nickname subject to personal preference and interpretation.
I've never heard or read about how/why the "Thanksgiving cactus" nickname came into being. When one considers the fact that store-bought specimens (at least the ones I've seen) are always labeled "Christmas cactus," "holiday cactus," or "Zygocactus," and nobody knows "it's really a Thanksgiving cactus" until someone tells them in a similar exchange to the one above, or they buy a plant with the botanical epithet on the tag and find the nickname by discrepancy investigating that, does it become an interesting question? Many common names are shared by 2 or more plants, but for these 2 plants (that need some assistance through asking someone or investigating/reading to differentiate,) someone felt the need to put "Thanksgiving cactus" into play.
Wondering passively about this is what made me start to feel awkward about being the one to say, "It's not really a Christmas cactus, it's a Thanksgiving cactus." Nobody uses that name except those who have had "the talk." And they understandably want to know, "How can that be true if I've never heard of that and it had a label that says "Christmas cactus?"" I never could find a good answer that wasn't just some lame version of, "because someone else says so, and I went along with it, so you should too." I don't see the point in it (and it made me feel pedantic, to quote Mr. Subjunctive on the subject, a form of insincerity I try to avoid when I catch myself doing it.) What do you think? Am I missing something? Lost my mind?
That is really cool. 
You must post it to the database if you haven't already.
in Feb. She proceeded to eat the plant. Chewed it up. I moved the plant into the hospital zone (lol) and watered it, pulled off most of the leaves that had holes and had been ripped. I thought it was a goner. It bloomed with only a few blooms in June (as it usually does, it is mid winter then here in Australia). Then the kitten ate it again. (stupid me put it back on the shelf).
