It does look like it - a closer view of the leaf sections would help. Very beautiful!

Looks like mine, mine is smaller and could be just the picture, but leaves are darker.

Yes in a general sense it is a Christmas Cactus. But people today divide them into Thanksgiving, Christmas, and Easter. I can't tell which it is from the picture. If it has 'horns' on its leaves, its a Thanksgiving, if there are none its a Christmas.

Schlumbergera x buckleyi, aka Christmas cactus - and a nice one, too.

Yes & it looks happy & well grown.

We moved to a new house a year ago that has a sunroom. My plants are going crazy loving it. We are now calling My "Christmas" a "holiday" cactus because it bloomed pretty much nonstop from Halloween thru this August. Its not blooming now but Halloween is coming up soon we'll see if it does that this year. I haven't done anything special with it. It is in a SE/S widow

Here is illustration of different 'holiday cacti':

There is difference in segments shape and in blooms - if your plant blooms, it is easiest to tell difference.

It's definitely a Christmas cactus; and you can tell that not only by the stem segments, but also by its growth habit: as it matures, Christmas cactus' stems exhibit a trailing or weeping tendency (as is the case with yours), whereas Thanksgiving cactus (S. truncata) has a more upright growth.

Mine's about 80 years old, and had gotten quite leggy over time, but I recently renewed it by cutting all the green stems where they attached to the woody stems, and re-rooted them in soil - the cuttings rooted up in no time. Here's what it looks like now.

Wow that’s so pretty!