All Cacti are succulents but not all succulents are cacti. Both Cacti and Cactuses is correct when referring to more than one cactus.
Most cacti live in extreme conditions and have adapted to store water and survive. The spines on cactuses are actually leaves. This extreme adaptation helps against water loss and protects the plant from herbivores.
There are approximately 127 genera in the family cactaceae with a large number of species of different shapes and sizes.