"I can't remember what type of desert the other large cactus, the organ pipe cactus, is located in."

Organ pipe are still more concentrated in Mexico, but I think some are in Arizona near the border.  I say "still" because many of our cacti are subtropical "invasive" species that have been moving north for thousands of years.  Regarding saguaro, they have "only" been in Arizona for around 9,000 years, about the same time as the first human habitations. 

How do I know?  I am a lead steward in a 36,000-acre Sonoran desert preserve, where I volunteer as an avocational archeologist and historian.  I also wrote a history of mining in the preserve that was privately circulated.