The shotgun is the Winchester M1887, the first successful repeating shotgun in the world. It was one of John Moses Browinings first commercialy successful designs, his third sale after the High Wall and the M1886 Big Bore lever rifle.
The design was really a modification of Christian Spencers carbine action, scaled up to take the 10ga 2 7/8" shell. There are actually a lot of them around because the production was overwhelmingly of cheep "commercial grade" guns with fluid steel barrels. Very few were made with the optional Damascus barrel, though enough were that you have to have any 87' you think of shooting checked out by a gunsmith first.
87's were made in 12ga as well, but after smokeless powder came out along with the M1897 pump gun only the 10 bore was made. A reenginered, smokeless powder capable version, the Model 1900 was built untill about 1914, in 10ga only.