I've seen the terms used unchangeably, but if I was to give a difference to them I would think the saddle blanket is something like a Navajo which really is a blanket, usually wool or a blend, and usually doubled up.
A saddle pad is just that, a thicker pad, sometimes made up of different materials, shaped to fit under the saddle.
A lot of people use the terms to refer to any blanket or pad-like thing that goes under the saddle and over the horse.
However, a blanket is just that - like a navajo or double weave blanket; they are usually folded over once to add thickness. I usually recommend having at least 2 blankets or a blanket over something like a wool pad.
A pad on the other hand is thicker and often times has more than one "component" to it, like a Weaver pad with gel or memory foam on the inside. You don't need anything else besides a pad when it's that good quality.
I have a thinner saddle pad that's just black and not pretty. If we are going someplace that I want to dress her up, I will put a colorful saddle blanket over the pad so we look purdy
I think the uses came up because western saddles unlike English couldn't be stuffed up to fit different horses. The western saddle size is what it is, it can't be taken to a tack shop and re-sized.
The western saddle sometimes needs a thin blanket for a well fit or small saddle and more padding up if its too big. Does that make sense?
I have both. Some pads are thin, some are thick. Nearly always they have at least 2 materials, the topside for pretty and the bottom side and will be sewn(quilted like) together. I prefer the ones with horsehair on bottom. I also have fleece ones. Not my fav.. Some of my blankets(yes they would be a woven material like a blanket) are thin(like the navajo ones) and I can use them alone on some horses, depends on saddle fit. I recently bought a blanket that is really thick.. I wont' be doubling that one up on anybody. The thin ones make great covers for couches for the doggies or sometimes throw rugs. ;)
If you cover your saddle with it be sure it's not in "varmit" range. Mice and rats will mess up your stuff when it's under cover much worse than when not.