An adult male horse if left intact is called either a "stallion" or a horse (sometimes full horse); if castrated, it is called a gelding. A rig or ridgling is a horse or colt with a retained testicle or one which has been incompletely castrated.
In the wild, colts are driven from their herds by the herd stallion somewhere between the age of one and two. This may be in part an instinct to prevent inbreeding. When driven out, they usually join with other young stallions in a bachelor herd. They stay with this band until they are mature enough to form their own herd of mares. The terms "rag" or "rake" have been historically used to refer to a group of colts, but they have fallen out of modern usage.
Webster's Collegiate Dictionary, fifth edition. G. & C. Merriam Co., Springfield: Mass., 1947.