Steel small arms ammunition cases were developed as a wartime contingency when strategic materials (copper, zinc, etc.) becomes short in supply.
The Allies manufactured it in massive quantities, as well as the Germans. Much of the US small arms ammo production in 1943-44 was steel cased, and again during the Korean War. The former USSR and it's client states have produced almost exclusively steel cases since WWII, with the idea that "wartime" production capability should be maintained. The US and much of western europe, being wealthier nations, uses brass cartridges as opposed to the Russians, Chinese, and their allies. One point that should be noted, is that small arms that are designed for use with steel cases have large, sturdy extractor designs, as steel cases have higher extraction forces than brass. Note that large, sturdy extractors are a signature characteristic of Soviet weapons designs.