From what I can tell, from the pictures, they appear as 32 S&W rounds. Introduced in 1878 (Cartridges of the World). My guess as to years of production are:
1. The box with the topbreak pistol pictured 1878 - 1890 or so.
2. The green label box with what appears UMC logo in a black oval 1890's - early 1900's
3. The red label box with what appears to be an UMC in a red meatball early 1900's until 1911.
4. The last box all tan with what appears be Remington UMC in the red meat ball 1911-1916.
In 1911 the Remington Arms Company and the Union Metallic Cartridge Company were combined forming the Remington Arms Union Metallic Cartridge Co.
In 1916 the name was changed to the Remington Arms Union Metallic Cartridge Company Incorporated which lasted until 1920.