A hinney is the result of breeding a stallion (horse) to a jenny (donkey). A mule is the opposite: a mare (horse) is bred to a jack (donkey). Both the mule and the hinney are sterile. For the sake of simplicity, both are referred to as 'mules'.
Hammer's dam (mother) was a Tennessee Walking Horse while Smokey's sire (father) was a Paso Fino. Both mules inherited the gaiting ability of their parents.