Carol, your red flowered one appears to be some type of Epiphyllum. Your pink flowered one is a Schlumbergera.
Nicki, Schlums are pretty tolerant of various media. I definitely would NOT recommend a gritty mix. If you were in Florida, with its high humidity and frequent wet periods that would be one thing. Schlums are true cacti BUT they are not from arid regions. Treat them as such and they will likely die on you. They are rainforest denizens and typically grow as epiphytes. Considering how low your humidity likely runs in the winter once the heat is turned on, I'd suggest you use an airy media that can hold some moisture. Like epiphytic orchids, they tend to want a very "breathable"/coarse media. A medium grade bark/coconut husk mix (with some combination of perlite, charcoal, hydroton, etc.) should work well. A little bit of potting soil can be added to that but, IME, isn't necessary.