During the stream, one of them said that they opted to go for a shotgun build because they had arc armour so I'm pretty sure mods are split into different sets.
Probably because the shotgun mods he had were meant for arc armor only. The whole point of this system is to use armor that you love the look of while at the same time making it how you want it to play. I'm almost 100% sure that mods will drop either as solar, void, or arc... and armors will drop in any of those as well, and you just have to match the elements together.