Stallion male horse
Mare female horse
Jack male of the ass family
Jennet female of the ass family
Mule cross between a male ass (jack) and a female horse (mare)
Hinny cross between a female ass (jennet) and a male horse (stallion)
Donkey nickname for the ass family
Burro Spanish for donkey

The only way to produce mules and hinnys is to breed horses and asses.
This is because mules are sterile due to an odd number of chromosomes.