This gets repeated a lot, but Guix really is not a fork of Nix. Not by any definition of "fork". Also not "a fork of sorts". The term "fork" only applies to one executable: "guix-daemon", which is a literal fork of "nix-daemon". They have, of course, diverged a lot, but this (and nothing else) is truly a fork.

Aside from this one executable there is no relationship between the two projects.

The daemon takes .drv files that list what preconditions a build has (= other .drv files), what build script to run (= a generated Guile script), and what outputs will exist when the .drv file has been processed. It processes these .drv files in an isolated environment (chroot + namespaces) where only the inputs mentioned in the .drv file are made available.

The drv files are not shared among the projects; they are not generated in even superficially similar ways. Guix is not a fork of Nix. "guix-daemon" is a fork of "nix-daemon".

Both are implementations of the same idea: functional package management.