Identification: weird zygocacti

I have many zygocacti. And only 2 of them never bloomed. Both of them were saved (previous owners threw them away). The 2nd one has thorns on its leaves (Zygocactus Opuntioides?). I would appreaciate any help.

 

Without a bloom, ID is going to be tough...

 

Since neither has crab-like stem segments probably neither is a zygocactus (Schlumbergera truncata) but rather other kinds that may require special treatment to flower. The one on the left looks like it may be a Christmas cactus (S. x buckleyi):

To ensure bud set for late December bloom, give plant cool night temperatures (50 to 55F/10 to 13C) and 12 to 14 hours of darkness per day during November

--Sunset Western Garden Book (2007, Sunset Publishing, Menlo Park)

Possibly the one on the right is something like an Easter cactus (Hatiora gaertneri). I have found this to be impossible to flower under ordinary indoor conditions whereas my crab cacti (zygocacti) flower regularly without special treatment.

 

If you can't find under Hatiora try Rhipsalidopsis:}