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Cacti are a specific family, and a type of succulent with sharp thorns, but succulents are more of a description of plants that have fat, fleshy parts (including leaves) which are evolved to live in dry condition. Not all succulents are cacti.
Succulents and cacti are special in that they can continue to photosynthesis in temperatures higher than that most other plants can tolerate. They can also be important stores of water in hot, dry habitats, providing food, shelter, and moisture for animal species which might otherwise not be able to survive.
Some species of birds specifically shelter and nest inside hollowed out cactus trunks. These tall cactus and their sharp thorns can help protect these birds and their offspring from snakes and other dangerous predators. In addition, some bird species have learned to use cactus thorns for impaling their prey, both killing the animals, and saving their bodies out of reach of other creatures, so they can be eaten later.
Both the cactus themselves and the species who rely on them represent biomass, and serve as biological carbon storage. Many people think of deserts as bare and dead, but the wildlife and microbes under the surface do in fact represent surprising biodiversity and carbon storage capacity. Interfering with deserts, both their soil and the organisms that live there can release carbon back into the atmosphere.
Much like bushes are used in cooler climates to create hedgerows, cactus can be planted along boarders so that they can grow together and form living barriers. In this role (just like with hedgerows) the cacti can help reduce erosion, while providing food and shelter to wildlife.
Arizona
BLM Arizona Weeds and Invasives Program "BLM Arizona has had a successful partnership with the Tucson Chapter of the Arizona Native Plant Society, working toward the control of buffelgrass in an area of the Ironwood Forest National Monument (IFNM) in an area where there is endangered cactus."