The 1894C is the .357 version. The plain 1894 is .44 Magnum.
I believe the 1894C is allowed in SASS, since it's a pre-1899 design that's chambered in a revolver caliber. Contact SASS to be sure.
The Cowboy has a 20" octagon barrel, a buttplate, and a slimmer foreend with an endcap. The 1894C has an 18.5" round barrel with a fatter foreend, a barrel band, a hooded sight, checkering, a rubber buttpad, and sling swivel studs.
I have the 1894C, but a non-checkered version, and a 39M with a tapered octagon barrel. Looks like the "cowboy" series. They didn't make many .22s like that, and it's been a long time since they did.
The longer, heavier, skinner gun might be a bit better for CAS, since it should be a tad more stable in the hands for rapid fire. The regular 1894C carbine carries lighter and points quicker, but neither is necessarily an advantage for CAS. I like mine, though.
BTW the 1894C sight hood is removable without tools. I believe you have to remove it for CAS.