Mexican snowball: When this plant was first discovered, it was like a lotus flower growing on the flat ground. The succulent leaves were covered with a layer of frost-like substance, like a round snowball. It was also a plant native to Mexico, so it was called Mexican snowball.
Hen and chicks: Like others of its kind, it produces multiple offsprings which can be separated from the parents in spring and grown separately. Hence, the common name, "hen and chicks", applies to several species within the genus, Echeveria.