Columbia Pricklypear, Columbia Prickly Pear, Hairspine Pricklypear, Many-spined pricklypear, Prickly Pear Cactus, Starvation Cactus: Opuntia X columbiana (Synonyms: Opuntia erinacea var. columbiana, Opuntia fragilis X polyacantha, Opuntia polyacantha, Opuntia polyacantha var. polyacantha) - Native.
Brown-spine Prickly Pear, Tulip Prickly Pear, Desert Prickly Pear: Opuntia phaeacantha - Introduced species. Unfortunately, this one has been mis-identified by numerous people as the native Columbia Prickly Pear.