It's not thick at all, it's an American term which allows a horse that shows the chacteristics of a breed to be registered with that breed society.
For insance a "Ranch" horse who's parents were believed to be Quarter Horses but who were never registered.
It allows the individual to get papers for the breed and compete at breed competitions, but it is a requirement that the horse be gelded or if it is a mare it must be spayed, so as it does not contribute to the breed in the future.