Anything in the cactus family can be grafted onto anything else in the cactus family, even jungle cacti to desert cacti. I've even grafted a Schlumbergera to a prickly pear. I would like to know, just because I'm curious and would like to experiment, is it possible to graft any cactus as a scion to a non cactus succulent rootstock?
Succulents, in general, are plants that have adapted to living in dry/arid/desert-like conditions. Cacti are a subset of succulents and are entirely native to North and South America and as such evolved very differently from other succulents in Africa/Asia. For one, they have spines whereas most others do not, and presumably, there are other physiological differences.
One of the most important factors in successful grafting is that the vascular systems of the rootstock and the scion be a close match. I don't know very much in detail about the biology of succulents/cacti, but given their isolated existence and independent evolutions, I highly doubt that you can graft any cactus onto any non-cactus succulent.