The definition of jennet varies depending on location and on the antiquity of the usage. It may mean a small Spanish horse, a female donkey, or a hybrid produced by a male horse and a female donkey, the opposite of the traditional mule-producing pairing of a female horse with a male donkey.
In the etymology provided by the 1911 Encyclopedia Britannica, jennet is derived from the French genet, from Spanish jinete, a light horseman who rides a la gineta, explained as "with his legs tucked up." The term is taken to be a corruption of the Arabic Zenata, a Berber tribe famed for its cavalry. English and French transferred the word from the rider to the horse, a meaning which the word has only acquired in Spain in modern times. The American Heritage Dictionary's etymology is similar, citing the Middle English genet, from Old French, from the Catalan ginet, of Arabic or Berber origin.*
Zoologists may casually use mule to refer to many kinds of sterile hybrids. However, among the general public, the term is understood to refer to a hybrid of horse and donkey. Such hybrids are usually, but not always, sterile. Among farmers and animal fanciers, mule is specifically understood to be the offspring of a male donkey, often called a jackass, and a female horse. The opposite pairing, the female donkey with the male horse, produces a mule in the general sense, but which is specifically identified as a jennet, jenney, or jenny in the UK and a hinny in the U.S.
As horses are much larger than donkeys, it is easier for a female horse to successfully carry and deliver the hybrid than it is for the much smaller female donkey. Although there are genetic and behavioral reasons as well, the size difference is the traditional reason cited to explain the relative rarity of hinnies in comparison to mules.