Tephrocactus articulatus var. papyracanthus is also classified as Cereus articulatus Pfeiff. 1837, Tephrocactus articulatus var. papyracanthus (Phil.) Backeb., Opuntia articulata (Pfeiff.) D.R.Hunt 1987, Opuntia andicola Pfeiff. 1837, Tephrocactus andicolus (Pfeiff.) Lem. 1868, Opuntia diademata Lem. 1838, Tephrocactus diadematus (Lem.) Lem. 1868, Opuntia turpinii Lem. 1838, Tephrocactus turpinii (Lem.) Lem. 1868, Opuntia papyracantha hort. ex K.Schum. 1898, Opuntia glomerata Britton & Rose 1919, Opuntia strobiliformis A.Berger 1929, and Tephrocactus strobiliformis (A.Berger) Fric 1933. Common names in use are Paper Spine Cactus and Paper Spine Cholla Cactus.