You have the ID's in reverse. 'The way you can tell the two apart is by looking at the edges of their flattened stems, which are called cladodes. The edges, or margins and Christmas cactus cladodes, above, tend to be somewhat rounded. Meanwhile, those of Thanksgiving cactus, at left, tend to be somewhat pointed.' Ettinger's
From link:
http://www.tlehcs.com/question...
I never saw one w/o a double flower. That will be something to see. My psuedo grandmother's plant is how I learned to love them too! Good luck!
Donna