- nix primarily is the package manager; basically can be installed anywhere. The big thing is; it builds packages to /nix/ , keeps software there and all the dependencies are done through symlinks to packages in the nix store - nix is also the functional programming language that the nix package manager can take as input - nixos is a framework for writing a system configuration in the nix language; and produces a working linux distribution; integrated with nix. - home-manager is copying the nixos framework, but brings it to userspace management.

The biggest issue getting into home-manager from outside is; it's high learning curve and due to being in the nix ecosystem; there is a lot of concepts that it uses (modules, configuration in functional paradigm) that is a whole lot to learn from 0 just to manage system config, but once things click together, it is wonderful.

To add to what you have found; there is also https://github.com/numtide/system-manager which brings NixOS' declarative system configuration to other distros as well, but I haven't personally used it.