According to “One Hundred Years of Winchester Cartridge Boxes, 1856-1956” by Ray T. Giles & Daniel L. shuey, your .44 Winchester box should date from between 1902 and 1905.

All I can tell you about the .22 Long Shot box is that it is from before 1911. It was in that year that U.M.C. and Remington Arms merged, and ammunition box labels reflected this merger by carrying the “Remington Arms – Union Metallic Cartridge Co.” name.

I hope this was helpful.