The name Christmas cactus is most often associated with a house plant native to Brazil, Schlumbergera, which has a stem that resembles jointed flat leaves with flowers on the end. See here for description.
But the real Christmas cactus, with red winter fruit and a green stem, is a native of the Sonoran and Chihuahuan deserts: a Cholla, Opuntia leptocaulis. This Christmas cactus, also called Tsejo, Pencil-joint Cholla, Holycross Cholla, Diamond Cactus, and Darning Needle Cactus, is a small shrub-like cactus usually about two feet high (but can get to five feet high) that likes to hide among other shrubs in the desert.
The round stem is just one-quarter inch in diameter but it supports a two-inch long spine in each areole as well as glochids (tiny hair-like, generally barbed spines, very irritating). Because the plant is inconspicuous except when in fruit, it commonly ambushes hikers.
Opuntia leptocaulis (aka Cylindropuntia leptocaulis) has half-inch pale yellow flowers that open in the afternoon and close by nightfall. The flowers are open for only three hours a day. The flowering season is May and June. Pollinators appear to be hummingbirds, honey-bees, and cactus bees.
This desert Christmas cactus has bright red mature fruit that persist through the winter. The normal range is Arizona to Oklahoma, Texas, and northern Mexico at elevations from 1,000 to 5,000 feet on desert slopes and in washes.
I have seen this desert Christmas cactus around Tucson, and I have a volunteer in my yard.
The fruit provides food for a variety of animals including quail and wild turkeys. White-tailed deer eat the joints. Both fruit and stem provide about 8 percent protein.