As they say, "That's a long story" Remington modernized gun barrel steel with the introduction of Bessemer process, or what they called Decarbonized Steel about 1846.
Modern high strength fluid steel started with Winchester Nickel Steel introduced in 1889 Remington Ordnance Steel in 1902 Marlin Model 21 Pump, introduced in 1907, had “Special Smokeless Steel” Most double gun makers used Belgian fluid steel for barrels until WW1 however
Some Browning patent Fabrique-Nationale-Herstal very early versions of the A5 shipped to the U.S. between 1903 and 1909 are marked Cockerill Steel.