A true mustang is a horse that is born in the wild, usually with at least one wild parent. If it goes back a couple of generations in the wild it will tend to show feral characteristics. It could have any type of horse in it's genetics, so there is no breed standard except that it be a wild born feral horse. It is generally acknowledged that the origins of the American mustang comes from the spanish Iberian horses specificly the Andalusian, and the Arabian as well as the Barb horses that were brought over by the Spaniards in their explorations. Many of these wild herds have had a lot of other stray horses including draft horses that have intermingled and kind of made a true "mustang" standard difficult to put in place. Thus, a mustang is a wild horse period.
That said, there are now some specific breeds of mustangs that do have certain standards, by type or conformation. Typically, a breed organization will define their particular type of mustang by these standards and you have to have them to register as such. Some orgs are fairly "loose" in their standards some not. Some of these include Spanish Mustang Registry, founded in 1957, followed by the American Indian Horse Registry, the Spanish Barb Breeders Association, and the Southwest Spanish Mustang Association. There are also a couple of registries that are very specific about what they allow in-most of which I can't remember at the moment. The two I can remember are the Cracker horses in Florida and the Kiger mustang. There are currently a couple of Kiger registries. The original Kiger registry only allows horses that were either from or descended from two areas near the Kiger range in Oregon. The Steens Mountain area and the Riddle area. These two particular herds are thought to be one of only a couple places in the country where the herds were so isolated that their bloodlines were never contaminated by other breeds or strays. This has been borne out by genetic testing. They do have certain standards for type, build, conformation, and must be able to prove that they have the Dun factor. So they are mustangs, even Colonial Spanish Mustangs, BUT not all mustangs or Colonial Spanish Mustangs could be a Kiger.