
A coyote attacking a sheep. His "elbow" is a couple of inches below the underline of his chest. Photo by U.S. Dept. of Agriculture, public domain.
One commonly cited difference is that a coyote has longer legs than a dog has. I've used that description myself, but I always felt a little uncertain. "Longer legs" isn't quite accurate. A coyote is somewhat longer than it is tall, and so is a typical dog.
No, a coyote does not actually have longer legs than a dog has. But there is an unmistakable impression of "legginess" about a coyote.
After puzzling over it for a while, I realized what it was. A coyote's "elbow" lies below the line of its sternum, and a dog's "elbow" is higher than its sternum. (There are rare exceptions, but I'll get back to that.)

The German shepherd has some resemblance to a coyote. His "elbow" is a couple of inches higher than the underline of his chest. Photo by Charles J. Bonner.
Now, why is this? Is the coyote's humerus proportionally longer than the dog's? Maybe so. But for field identification purposes, it is not really necessary to take precise measurements.
Look very closely at pictures of coyotes and dogs, and you will see that the real difference is that the dog's chest is proportionally deeper than the coyote's.
The same is true in other wild canids. Domestic dogs have deeper chests than foxes, wolves, or jackals.
The gray wolf is the most equivocal of the wild canids in this regard. A gray wolf's chest is a bit deeper than that of a coyote, and its elbow joint is just about on the same level as the underline of its chest. This can be rather hard to distinguish when the wolf has long fur, as they often do.

The Boston terrier doesn't look anything like a coyote. Still, his "elbow" is distinctly higher than the underline of his chest. Photo by Charles J. Bonner.
What about those exceptions I mentioned earlier? There are two, the sighthounds, and the "primitive" domestic dogs.
In most sighthounds, the elbow joint actually is lower than the underline of the chest. This is obviously not a matter of having a shallow chest. Sighthounds have proportionally longer humerus bones than other dogs. Still, nobody is going to mistake a greyhound for a coyote.
"Primitive" dogs also often have the elbow joint lower than the chest. They retain the same proportions of chest depth and leg bone length as their gray wolf ancestors.
Fortunately, most primitive dogs are strikingly different from coyotes in other characteristics. Most "pariah" dogs are yellow, and many also have drooping ears and/or curled tails, which coyotes and other wild canids never have. And these primitive dogs are very rare in the U.S., where coyotes live, and you'll never see one roaming free.
Next time you think you see a coyote, try to get a good view of the front legs and see where the "elbow" joint is. A coyote has a very "leggy" look that comes from a shallow chest.