Linux

You're actually right that it seems to use parts of it:

It uses low-level mechanisms from the Nix package manager, but packages are defined as native Guile modules, using extensions to the Scheme language—which makes it nicely hackable.

As such, the packages look largely different:

(define-public hello
  (package
   (name "hello")
   (version "2.10")
   (source (origin
            (method url-fetch)
            (uri (string-append "mirror://gnu/hello/hello-" version
                                ".tar.gz"))
            (sha256
             (base32
              "0ssi1wpaf7plaswqqjwigppsg5fyh99vdlb9kzl7c9lng89ndq1i"))))
   (build-system gnu-build-system)
   (synopsis "Hello, GNU world: An example GNU package")
   (description
    "GNU Hello prints the message \"Hello, world!\" and then exits.  It
 serves as an example of standard GNU coding practices.  As such, it supports
 command-line arguments, multiple languages, and so on.")
   (home-page "https://www.gnu.org/software/hello/")
   (license gpl3+)))

vs

{ callPackage
, lib
, stdenv
, fetchurl
, nixos
, testers
, hello
}:

stdenv.mkDerivation (finalAttrs: {
  pname = "hello";
  version = "2.12.1";

  src = fetchurl {
    url = "mirror://gnu/hello/hello-${finalAttrs.version}.tar.gz";
    sha256 = "sha256-jZkUKv2SV28wsM18tCqNxoCZmLxdYH2Idh9RLibH2yA=";
  };

[...]

  meta = with lib; {
    description = "A program that produces a familiar, friendly greeting";
    longDescription = ''
      GNU Hello is a program that prints "Hello, world!" when you run it.
      It is fully customizable.
    '';
    homepage = "https://www.gnu.org/software/hello/manual/";
    changelog = "https://git.savannah.gnu.org/cgit/hello.git/plain/NEWS?h=v${finalAttrs.version}";
    license = licenses.gpl3Plus;
    maintainers = [ maintainers.eelco ];
    mainProgram = "hello"; 
    platforms = platforms.all;
  };
})

Also note that NixOS' repository is one of the biggest among all distributions while Guix System only hosts free software.