Sometimes the labels on plants are less than enlightening, and often the confusion gets even worse when I start looking them up. I'm not sure about the common names applied to either of these cactus, but they both do seem to be related and are maybe different forms of the same species.
The cactus in the picture below was labeled "Peruvian Torch" Cerus peruvianus. When I first purchased it I thought the new growth at the base, was a different type of plant, but as those little leaves grow I am wondering if they won't fatten into the same shape as the main plant.
I bought this next cactus around the same time as the one above and it was labeled "Curiosity Plant" Cereus peruvianus monstrose cristate. It appears to be similar to the one above except it is covered with golden spines.