There are a number of differences between a mule and an ass, but the main difference is the number of chromosomes: an ass or donkey has 62 and a mule has 63. A mule is the offspring of a horse and a donkey, but mules cannot breed.
Mules are not considered an independent hybrid species because they are normally sterile while donkeys are their own species. Both male and female donkeys can be bred, but it is far easier to breed a male donkey with a female horse than the other way around. Donkeys can be traced all the way back to the ancient Egyptians and were brought to the Americas by Christopher Columbus. Mules are more intelligent than donkey's or horses.