No, Docker doesn't maintain systems, it handles applications. No one runs systems inside of Docker. People run applications with Docker, and Docker itself runs on systems.
And no, Nix doesn't "do this differently and better", as what Docker does and Nix does is wildly different. Nix is for machines, not applications. Sure, a subset of features from Nix can be used like Docker, but that doesn't mean Nix and Docker is the same, no matter what you think of markets or whatever.