Anybody know the correct name for this flowering cactus?

[gnathaniel]

It's not really a 'cactus-OR-hybrid' distinction as there are hybrid cacti and species euphorbs. They simply belong to different botanical groups (Cactaceae and Euphorbiaceae) that aren't closely related but have in some cases evolved similar morphological traits in response to similar habitats.

Be careful handling the plant when cut, the milky sap is toxic in many euphorbs and in some species can be irritating or dangerous to the skin.

[orchidsarefun]

As a kid in Zimbabwe, we had these growing in the "rockery"/garden. We called them Christ-thorn, which I suppose is now the more PC Crown of Thorns. Ours were red and I remember them growing into a 4 ft tall hedge...