The word sage covers a genus of roughly a thousand species and at least three separate traditions that are routinely run together.
Salvia officinalis, garden sage, is the Mediterranean culinary and medicinal herb described above, and the plant Culpeper meant.
White sage is Salvia apiana, a distinct species of southern California and northwestern Mexico. Its use in bundled form as a purifying smoke belongs to specific Indigenous Californian and Southwestern practices and is not a European tradition, not a Culpeper tradition, and not interchangeable with garden sage. The popular association of smoke cleansing with the word smudging, itself a term of contested application, reached the general market through the twentieth-century New Age trade, and the resulting commercial demand has produced documented problems of overharvesting on public and private land in California and of objection from several Native nations to the sale of the practice. Describing Salvia apiana as though it were an ancient European herb, or as though its ceremonial use were freely available, gets both the botany and the provenance wrong.
Clary sage is Salvia sclarea, grown for an essential oil used in perfumery, and Salvia divinorum is a Mexican species containing salvinorin A, a potent and pharmacologically unusual hallucinogen with a documented Mazatec ritual use, related to the others only by genus.
The word sage in a correspondence table nearly always means officinalis. It is worth checking, because the table rarely says.
Sources The Appropriation of Native American SpiritualitySuzanne Owen with Plants of the World OnlineRoyal Botanic Gardens, Kew