Zebras belong to the genus equus. This is the only genus that has living species under the family equidae. The genus includes horses, donkeys, and zebras. Within the genus, there are many different species. Some of them include the equus quagga quagga and the equus ferus caballus. The first is an extinct species of zebras - even though there are a lot of efforts being done to see if these could be brought back to life - and the second is a species of horse.
Equus in and of itself means to some kind of herbivorous animal, often with a long neck and a tail. Many of these species have manes that stand up straight and an odd number of toes on their feet, if they have toes.