What is the genus and species of domestic cats?

The domestic cat is of the genus Felis.

Other genera of the cat family, Family Felidae include:

Acinonyx (cheetah)

Caracal

Catopuma

Leopardus

Leptailurus (serval)

Lynx

Neofelis (clouded leopards, 2 species)

Panthera (jaguar, lion, leopard, tiger)

Profelis

Puma

Uncia (snow leopard)

There are about 38 species in Felidae in total.