If you've turned to a system based on everything being perfectly declarative and reproducible, why would you then add an imperative autoupdating system on top of that? Of course you can, but if you're fine with that kind of system, why would you have turned to guix in the first place? It's not like it's just the popular default and you want to do something else on top, it's a super niche thing based specifically around this and you're breaking the core philosophy

I had the impression, Guix was a package manager and GuixSD the OS?

It is all just Guix now. It's both package and systems manager.

The OS is called "Guix System". Without the system part it's just "Guix".

Both variants are very similar. The Guix tool comes with a "guix system" command, which lets you build Guix System containers, container images, system images, qemu VM images, qemu VM scripts, etc. The only command that won't work on a "foreign" distro is "guix system reconfigure" --- but that's only a "guix system init /" away ;)