Winchester had a whole series of Self-Loading rifles before WW I.
They started out with the 1903 in .22 Winchester Auto. A distinct cartridge so you would have to buy the right smokeless ammunition and not gum up the action with still-common black powder .22 lr. They later brought out the design as the Model 63 in .22 lr Super-X and Super Speed after smokeless was pretty well standard. They looked and operated similar to the 1907 you show except for a tube magazine in the butt.
The 1905 was made in .32 WSL and .35 WSL. Whose best feature was that the .30 carbine was later based on .32 WSL.
For more power they brought out the 1907 in .351 WSL, more powerful than .35 WSL and not interchangeable. A picture of period ammo and box at
http://www.ammo-one.com/351WSL.html
The '07 (and 63) lasted longer than the rest, made until 1957. It was a popular police and prison guard weapon with the ten shot magazine you show first. The five shot was standard and plenty for hunting.
For still more power they added the 1910 in .401 WSL; about as powerful as a .30-40 Krag but shorter ranged with stubby RN bullet.
So each model had its own distinctive ammunition, not used in any other rifle I know of. They are all straight rimless or semirimmed cartridges not derived from any other. Which makes the guns kind of expensive to shoot.
Oh, yes. They are all blowback operated, with a forward bolt extension inside the foreend to add reciprocating weight. A BIG extension with the centerfire cartridges, the guns are not as light and handy as they might look.
