"Dragon's blood" was never one substance. Merchants sold whichever deep red resin was to hand under the same dramatic name, and at least three unrelated plants answered to it across different regions and centuries, a confusion the trade never bothered to resolve.
Traditional Chinese medicine calls its version xue jie and classifies it, like myrrh, as a blood-moving herb used to close wounds and treat pain from bruising and stagnation, a functional medical role rather than a magical one.
On the island of Socotra, off the Horn of Africa, the resin comes from Dracaena cinnabari, a tree found nowhere else on Earth, and the local population has used it as a dye, a medicine and a ritual pigment for a long documented history predating any European trade in the substance at all.
The plant now most associated with the trade name in modern retail, several rattan palms of the genus Daemonorops from Southeast Asia, became the dominant European source only from the medieval period onward, when the fruit resin proved easier to ship in bulk than either the Socotran tree sap or a fourth candidate entirely, the unrelated South American genus Croton, whose sangre de drago is a distinct traditional medicine in its own right and not simply a New World dragon's blood.
Modern folk magic mostly ignores all three histories, adding a pinch of whichever is sold to intensify other incenses rather than burning it alone, a use that predates none of the traditions above and borrows from all of them equally.