Not two names for the same animal
A donkey is a true species: a domesticated ass, born of two donkeys and able to breed with another donkey. A mule is a cross — specifically the foal of a mare, a female horse, crossed with a jack, a male donkey. The reverse cross, a stallion on a female donkey, produces the rarer and usually smaller hinny. Because horses and donkeys carry different numbers of chromosomes, the mule inherits a set that cannot pair up properly, which is why mules are almost invariably sterile. So the difference is not size, colour, or temperament: one is a species, the other is a hybrid, and everything else about them flows from that.
Telling them apart by eye and ear
Both have long ears compared with a horse, but the mule's build betrays its mother: a mule tends to have a horse-shaped body on slimmer legs, a mane that stands upright but thinner than a horse's, and a tail tufted like a horse's rather than the donkey's thin, cow-like tail with a tuft only at the end. Donkeys have a distinctly narrower, more upright body, a dorsal stripe with a cross over the shoulders in many colours, and small, hard, upright hooves. Their voices differ too — a donkey produces the full two-tone bray, while a mule often starts with a whinny and ends in a bray, or brays less altogether.
Temperament: self-preservation in two styles
Both animals have a reputation for stubbornness that is really a strong instinct for self-preservation, but it shows differently. A donkey tends to freeze and assess when unsure, and will plant its feet rather than flee; pushing one through fear usually makes the stand-off worse. A mule combines the donkey's caution with a horse's quicker reactions, and many owners find mules exceptionally intelligent, long-memoried, and quick to learn routines — including which gate latch is weak. Both bond strongly, and both punish rough handling by withdrawing cooperation, sometimes for a very long time.
Feeding, feet, and workload
Donkeys evolved for sparse, dry country and thrive on coarse, low-sugar forage; rich pasture and generous grain rations make them fat and put them at risk of laminitis and liver problems, so a donkey's good life looks plainer than a horse's. Mules, being part horse, usually need somewhat more than a donkey but remain thriftier than a horse of the same size. Donkey hooves grow at a different angle from horse hooves and need a farrier who trims them upright rather than copying a horse's foot. Both animals are famously sure-footed and strong for their size, and a well-matched mule can carry or pull loads over ground a horse would struggle with.
Choosing between them
Pick a donkey if you want a companion, a guard animal for sheep or goats, or a driving animal on a smallholding with modest grazing. Pick a mule if you want a riding or pack partner with more size and athleticism while keeping the hybrid's hardiness. Either way, the animal's identity should be recorded accurately, because feeding, hoof care, and breeding expectations all hang on it — and if you rehome one through KinsLe, its Transferrable Profiles record moves with it, telling the new owner plainly whether they are taking on a species or a hybrid.