There are not any differences as written. Using the mule statistics for donkeys seems reasonable enough, given that D&D isn't really meant to finely model the abilities of real-world creatures (and they mostly have statistics at all simply for the case of fighting 'em). The Monster Manual (appendix A) says:
A book of this size can’t contain statistics for every animal inhabiting your D&D campaign world. However, you can use the stat block of one animal to represent another easily enough. For example, you can use the panther statistics to represent a jaguar, the giant goat statistics to represent a buffalo, and the hawk statistics to represent a falcon.
The difference between "giant goat" and "buffalo" probably exceeds that of mule to donkey.
If this doesn't feel satisfying, though, I think it's reasonable to work with your DM to modify to taste. As long as you're not giving it a +10 2d12 gore attack and firebreathing, I can't see why anyone would really make a fuss.
(If you do want to make your own, my offhand thoughts: Remove the Beast of Burden feature, drop its strength and raise its dexterity, and drop its attack damage too. Maybe give it more charisma, because those ears are so cute.)