Cacti have either a long tap root or fibrous roots just below the surface of the ground.
It's spelled cacti. The plural form of cactus is like the plurals for octopus and pegasus (e.g. octopi and pegasi). These particular words are spelled in exactly the same way as their Latin root words would be, so the us is changed to i.
One cactus, two cacti
Some cacti have a tap root while others have a dense fibrous root system.
I water my Mammillaria cacti once the soil has dried out completely. This is recommended for all cacti, it is better to water them not as often rather than regularly because if you get root rot then your cacti will die.
tap root
Stop Watering it, let the soil dry out between waterings
cactus for a single plant cacti for plural
You could suppose that cacti of the same type look similar. They will have the same color patterns and spines, but will most likely be shaped differently.
CAM
scorpions cacti
No cacti store water, not milk. A genus of succulent called Euphorbia leak a milky latex when damaged, they look like cacti but are not. This is probably what you are thinking of. The latex produced by plants in the genus Euphorbia is a skin irritant and can cause temporary blindness. They are common in cacti collections, and are often sold as cacti.