Is this related to the rosemary bush, grown in dry, sandy soil?
yes, this is the plant often called wild rosemary bush, also called Sand heath and Florida rosemary, Ceratiola ericoides. It is becoming scarce because it is almost impossible to transplant and its habitat is disappearing, so it should always be protected where it is found. It is not actually a rosemary that we use in cooking, but it is in an unusual family called the Empetraceae, our only member of that family here in South Carolina, in the sandhills. It seems to be a remnant of the time that the sandhills were sand dunes along the coast when the ocean level was much higher. It is very well adapted to deep sands in hot, exposed areas, but dies and dries quickly when it is disturbed. A plant to be valued!
Steve Hill, Ph.D., Botanist, SCNPS