As one would expect the names given above to the little beast of burden are synonymous and used interchangeably in reference to the animal under the Latin title of Equus Asinus.
Webster defines a donkey as a domesticated ass but is often used to describe a stupid or foolish person.
Webster defines an ass as a horse like animal with long ears and a short mane. It also is used to describe a stupid or silly person. The ancient name of ass or donkey is referred to in the Bible in both the Old Testament and the New Testament many times.
Webster defines a burro as a small horse or a donkey.
In Spain the animal was given the name of “el burrito.” By the time “el burrito” came to South America and Mexico, its name was shortened to simply “burro.” The name burro stuck when it migrated north to America though ass and donkey are also used.
Some clarification:The burro is not a mule. According to Webster a mule is the hybrid off-spring from the liaison between a male donkey, (jack), ass or burro,whichever name you chose, and a female horse (mare). The resulting offspring is called a mule and is generally sterile. Webster also gives reference to mule as a stubborn person. Could this be where mule-headed got its roots?
Wikipedia describes the “hinny” as the domesticated equine off-spring of a horse (stallion) and a female ass, burro, donkey and it is also considered sterile. The hinny is often smaller in stature than a mule and its head resembles a horse more so than a mule and its ears are a little shorter. Tail and mane also favor more of a horse look than a mule. The hinny is often called a Jenny or Jennet.
The sterility of both the mule and hinny are attributed to their chromosomes. A Horse has 64 while the donkey, ass, burro has 62. The mating results in an offspring with 63. The odd number is the reason for virtual but not impossible reproduction. Some rare cases of mating mules with donkeys have produced a foal.

Now back to donkeys, asses and burros.
Webster defines a jack-ass as a male donkey.
The unhyphenated word jackass is often used to denote a fool or stupid person or his doltish antics as depicted in the 2002 movie “Jackass.”
A Jennet is defined as a female donkey or ass.
The vast desert areas of Texas, New Mexico, Arizona, Colorado, Idaho, Utah, Nevada and California are a natural homeland to the donkey. Some say that a donkey is smarter than a horse and able togo without food and water longer (four days) in some documented cases. Most horses would not make it that long in a harsh overheated desert environment.
Traditionally, desert prospectors, when lost, could simple turn their donkey loose to roamthen follow the animal to an oasis of some sort. The crafty little animal, unlike a mule that requires grain, is a forager and wouldmost likely nibble cacti or sagebrush along the way. Sooner or later he’d go where there is water.
Personally, I have owned but two donkeys. One male (jack) gelded and one female (jenny.) My friend and I wanted to take our sons into the Marble Mountain Wilderness area of Northern California and do some real back to nature camping; none of that RV camping for us. We figured we might need a little help in transporting the camp goods. If you’ve ever hoisted and carried a forty to fifty pound backpack for a few hours, you’ll know what I mean. I wanted eggs for breakfast and potatoes at night. None of that freeze dried or powdered stuff for us. The goodswe wanted to take along began to add up both in weight and bulk. We planned to take food for five days, cooking utensils, first aid kit, extra clothes, fishing gear, sleeping gear, some animal feed, a tarp and a bottle of hooch.
We bought the male donkey, that we named “Bucky,” on a whim and borrowed another older male along with lead ropes, wooden Sawbuck pack saddles and canvas panniers. We didn’t have any horses to ride and figured to hike and lead the donkeys along just like the early day prospectors did.
When we arrived at the trailhead, we saddled both animals then loaded the panniers, distributing the weight equally on either side. With lead ropes in hand we started out. We were a couple of greenhorns then, (I still am)and soon learned a few valuable lessons.
Donkeys do not like to cross over wooden bridges without a little or a lot of coaxing. Thinking back, perhaps a little,unimportant at the time, pre-training would have helped. There are lots of wooden bridges, many only three feet wide, along the national forest trails. I think the noise of their hooves on the planking is what gets them to balk as if stepping on ice. Otherwise our adventuresome trip to a pristine mountain lake was going along fine.
By afternoon of the second day we were sweaty and trail weary and had all stopped to have a rest alongside the trail.
Bucky decided that it was time for a good ole roll in the inviting dusty trail. I mean we were relaxing, why couldn’t he? Of course Bucky didn’t see fit to have the saddle and panniers removed, so consequently what loafed bread he carried in the packsproved to be a little squashed. I believe that I had a few choice epitaphs for Bucky’s earswhen this old photo was taken. To further our chagrin,Buckywanted to have his rolled oats at the crack of dawn and blasted us from our sleeping bags, with his braying, every morning until he got them!
Either I or my partner used Bucky several more times on like trips but we learned to strip Bucky of the packs before he got it into his head to take a roll. I like donkeys very much, despite their sometime cussedness. There is a lot of documented history exhibited in books and movies (Treasure of the Sierra Madre)containing the use of donkeys, asses, burros and a lot of fiction to go with it.The animals in my care exhibited a gentle nature and never balked at taking a trip. I’ve often said that I would have a herd of them if I had the facilities. I salute the hardy beast.
For an in depth study and some fine reading about donkeys I recommend William G. Long’s book “Asses Vs. Jackasses” published in 1969(currently out of print) later reprinted and renamed “Donkeys of the West in 1974.”