@JakeEkiss This is a good explanation as well, but actually not the way my head canon worked.
In my mind, Steel Corps/Steel Brigade are kind of like 'Joe Reserves.' They're top level soldiers/marines that get 'called up' to serve with the Joes for specific purposes, but then get disbanded back to their regular units after the mission is over. They hide their faces because, unlike Joes, they've gotta go back to their units and be regular people again, and don't want their faces on the news or, more importantly, Cobra's computers.
Greenshirts, as said, would be actual Joes-in-training, with the intent of becoming full-time members with all that entails. Although, again just in my own head canon, Greenshirts can also just be support staff. Either people that couldn't make it as a full-fludged Joe for field ops, Greenshirts that took an injury in training to become a Joe and needed to be sidelined, etc. Once you know your way around the Pit, makes more sense to keep you even if it's just delivering food and helping with oil changes.