I'm still confused. What is Nix? Is it an OS, or a package manager? From the looks of it it's a package manager that I should be able to use it on any POSIX system, but I doubt that's the case?

What is Nix?

Nix is a powerful package manager for Linux and other Unix systems that makes package management reliable and reproducible. It provides atomic upgrades and rollbacks, side-by-side installation of multiple versions of a package, multi-user package management and easy setup of build environments.

What is NixOS?

NixOS is a Linux distribution with a unique approach to package and configuration management. Built on top of the Nix package manager, it is completely declarative, makes upgrading systems reliable, and has many other advantages.

[1]: https://nixos.org/

Thanks, but that makes me wonder how that's even possible given that distros make their own modifications? Do people port each distro's packages to Nix then? Are they kept up-to-date? Or does it automatically translate from apt/pacman/etc. databases somehow? Or does it just basically install vanilla packages on all distro?

Yeah, there is a giant repo of package definitions at https://github.com/NixOS/nixpkgs. Those definitions tell nix how to build everything from the ground up.