They get green when they are full of water and then dry out, turning grayish green.

Actually, things have changed since I learned that. From the Joshua Tree National Park Website:

https://www.nps.gov/jotr/learn/nature/jtrees.htm

Known as the park namesake, the Joshua tree, Yucca brevifolia, is a member of the Agave family. (Until recently, it was considered a giant member of the Lily family, but DNA studies led to the division of that formerly huge family into 40 distinct plant families.) Like the California fan palm, Washingtonia filifera, the Joshua tree is a monocot, in the subgroup of flowering plants that also includes grasses and orchids. Don’t confuse the Joshua tree with the Mojave yucca, Yucca schidigera. This close relative can be distinguished by its longer, wider leaves and fibrous threads curling along leaf margins. Both types of yuccas can be seen growing together in the park. The Joshua tree provides a good indicator that you are in the Mojave Desert, but you may also find it growing next to a saguaro cactus in the Sonoran Desert in western Arizona or mixed with pines in the San Bernardino Mountains.

So, neither a Lily nor a Cactus.