Hellraiser and Iggy are right on.
Being a hybrid cross between a mare and a jack, there are a lot of variables to a mule that can be thrown into the mix that makes up a mule's anatomy.
The big difference between a saddle built on a "mule tree" and a saddle built on a "Quarter Horse tree" or "Semi-Quarter Horse tree" is the angle of the bars. Depending on the individual mule, most Quarter Horse saddles are too wide sprung on the front for a mule at the shoulder.
So, if you place your typical riding saddle (most are usually built on "Quarter Horse trees" or "Semi-Quarter Horse trees") on your mule, it will usually fit up there towards the top or gullet of the saddle. But, if you slide your hand down between the mule and the saddle, starting at the gullet and going down to where your breast strap attaches, you'll feel where the contact pulls away slightly from the mule.
So, when you climb into the saddle, all of your weight is on top of the mule's withers because there's no support in the shoulder.
Another difference in the two saddles is what saddle makers call "pitch." Your typical horse saddle will generally have more pitch when it leaves the twist of the saddle tree. The twist of the saddle tree is the point of the tree that is leaving the withers area and starts the rib cage. Mules are usually flatter than a horse through the rib cage, but not necessarily so. I've got one molly mule (i.e. female mule) whose rib cage is so sprung you'd think she was pregnant.
The last big difference between the two saddles is what is referred to as the amount of rock or bow between the front and back of the tree. Mules don't need a lot of rock in a tree because they normally don't have that pocket behind the withers like horses have. You look at a mule's back and you can see where it is almost flat, whereas a horse has a pronounced withers.
Anyway, that's probably a heckuva lot more than you wanted to know.
Also, like Hellraiser pointed out, if you're riding a mule, you'll want either a crupper or a britchen, along with a breast strap. Saddling some mules is kinda like putting a saddle on a pig. If you don't secure it from both ends as well as around the middle, you'll either go shooting over the neck or slipping off the rump.
The McClellan saddle was usually issued with a britchen attached. I have an old McClellan that still has remnants of the original britchen.
The old McClellan saddles won't normally fit today's horses. The McClellan will pinch the heck out of your typical modern-day horse's withers. The horses of the 1800's and early 1900's were typically a little narrower in the shoulder and spine area.
Here's a picture of your typical saddle mule rig. He's got a breast strap to keep the saddle from slipping off his back when he's climbing hills, and a britchen to keep the saddle from pinching his shoulders when he starts headin' downhill.
You normally can't tell the difference between a horse saddle and mule saddle unless you strip off all the leather and look at the tree. But believe me, if your saddle doesn't fit your horse or mule, it won't take long before you find out. He'll either start pitchin' a fit, or when you unsaddle him, you'll find some gosh awful sores on his back. (By the way...soring your horse or mule up like that is a hangin' offense in some circles.)
Iggy brought out a real good point that I wish more people would pay attention to...and that is, you fit the saddle to the animal
first!!! Too many people go out and buy the first saddle that catches their eye with no regard as to whether or not it's gonna fit ol' Thunderbolt.
Oh well...time to get off my soapbox.
