From The Manufacturer/Wikipedia/People Smarter Than Us:
Designed by John M. Browning to replace the Model 1873, the 1892 Winchester rifle became one of the most popular lever actions of all time. It was based on his Model 1886, but reduced in size and chambered for the popular short cartridges used in the Winchester 1873. Simplification of the elevator and feeding system gave the 1892 a much smoother action than previous models. While earlier rifles and shotguns may have actually Won the West, the majority of lever action rifles seen in classic Hollywood Westerns are Winchester 1892 carbines and rifles.