A NixOS config is a bit different because it’s lower level and is configuring the OS through a first-party interface. It is more like extending the distro itself as opposed to configuring an existing distro after the fact.
The other big difference is that it is purely declarative vs. a simulation of a declarative config a la Ansible and other tools. Again, because the distro is config aware at all levels, starting from early boot.
The last difference is atomicity. You can (in theory) rely on an all or nothing config switch as well as the ability to rollback at any time (even at boot).
On top of all this are the niceties enabled by Nix and nixpkgs. Shared binary caches, run a config on a VM, bake a live ISO or cloud VM image from a config (Packer style), the NixOS test framework, etc.