It's similar n some way, but totally rethinking the problem.
Ansible or saltstack are essentially programs that configure your system in specific way. Ansible takes more of a list of things what to change and how, while saltstack tries to be declarative.
NixOS is essentially a Linux system described using Nix language. Whenever you make change and run nixos-rebuild, as name suggests it actually rebuilds your entire system from scratch, it is just smart enough to not do work that was already done.
Benefits of it is that you will always get to the same state no matter what. Another benefit that is quite annoying with saltstack/ansible if you remove specific application/service/whatever once you rebuild the system, it is gone, like it was never there.
You also get Nix benefits, nix never leaves anything in half state changes are atomic, either they are applied successfully or not, if a change broke something, you can easily rollback. Things like for example changing KDE to Gnome or replacing Xorg with Wayland is no harder than replacing emacs with vim (or vim with emacs, if I upset you).
The way how Nix works allows different packages using even conflicting libraries. For example you can have two applications using different openssl version etc.
If you have one application and you need to apply a custom patch to it or maybe even use a different version. In traditional OS good sysadmins would create a custom RPM package an install it. In Nix you just override the definition, and if a cached build is not available, Nix will be smart enough to compile the code (this means no need for artifactory and uploading custom packages there, though to prevent recompiling every time, you should set up a caching server (there's also caching as a service option if you don't want to manage it) or you can even use S3 bucket.
Basically Nix and NixOS is rethinking how building/deploying/packaging does it offers many benefits, CMS like ansible/saltstack/chef/puppet/cfengine etc are no longer needed. It can be used for having comon developement environment, can be used for building, ci/cd etc.