Real Dictionary

rein
plural noun: Journalists sometimes use the expression the reins or the reins of power to refer to the control of a country or organization.
plural noun: Reins are the thin leather straps attached round a horse's neck which are used to control the horse.

rein in American English
a narrow strap of leather attached to each end of the bit in the mouth of a horse, and held by the rider or driver to control the animal
noun: a leather strap, fastened to each end of the bit of a bridle, by which the rider or driver controls a horse or other animal by pulling so as to exert pressure on the bit

rein in British English
noun: one of a pair of long straps, usually connected together and made of leather, used to control a horse, running from the side of the bit or the headstall to the hand of the rider, driver, or trainer