What is the difference between a zorse and a hebra?

A zorse is the result of a cross between a male zebra and a mare. A hebra is the offspring of a male horse and a female zebra. I think the difference in nomenclature is because the cross between a mare and a male donkey produces a mule, whereas the cross betwween a male horse and a female donkey does not create the same thing... It produces a hinny which looks more like a horse than a donkey. Therefore, different names were created depending on which animal was the sire and the dam.