I’m guessing when you say cathedral cactus you‘re talking about Euphorbia trigona? Yes, that will work fine for Euphorbia grafting;). Here‘s some other suggestions from the International Euphorbia Society: ”Strong growing stocks are E. ingens, E. candelabrum, E. canariensis, E. grandicornis and E. trigona. A moderately strong stock is E. fruticosa. A less vigorous but reliable stock is E. obesa. E. mammillaris, which is often used, is reliable but seems short-lived. For the caudex-forming Madagascan euphorbias, such as E. capsaintemariensis, E. moratii, E. primulifolia or E. ambovombensis, Rauh (1987b) recommends as a stock E. milii var. hislopii.”

As with so much of taxonomy, whether or not there are differences between the two is debatable. There are some who hold to considering the two terms as separate/distinct and others who believe they are one and the same. (Members of the latter group generally advocate dropping one of these terms from usage.) Supporters of their usage essentially view the matter this way: In both convergent and parallel evolution, similar environmental pressures can led to similar morphologies amongst diverse organism living in those conditions. Parallel evolution is when this occurs with unrelated organisms or organisms that are so distantly related they can be considered "unrelated." (An example would be the Gymnosperms (conifers and their close kin) and Angiosperms (flowering plants).) Convergent evolution is when this event occurs amongst related organisms. Just how far back one has to go for the evolutionary distance between two groups leads them to be considered "unrelated" I have no clue. There is a short article here >>> article. If one reads the section on homology and homoplasy, one will find the author's take on cacti and Euphorbia.

It is, as Kara ID-ed it, Senecio stapeliiformis. No hard spines, no hard ridges and flowers - if any - very different from euphorbia or cacti. Here is my plant. One of the stems was broken, but now is growing a new 'arm' (photo on left). I stuck damaged tip into gritty mix, and it already rooted and also seems to grow a new 'arm' (photo on right):

Step one follow @hoovb zone 9 sunset 23 advice. Check the roots Step TWO!!! MOST IMPORTANT Get it out of the potting mix that it came from. What works in a greenhouse does not work in a house. They use the same mix for all of the plants they grow, annuals, perennials, succulents, tropical plants. It all works in those hot, sunny greenhouses. I've worked them, I know. The pot also seems a little small. The little guy is probably crowded out. Being smaller, probably planted latter in the pot, it can not compete with two massive neighbour that steal all that need and steal all the resources. If you put them all in a new pot, you can space the little guy out a little further from the other two. It will give him a chance to put down from good strong roots.