The most obvious difference going from Debian stable to GNU Guix is that Guix is a rolling release distro, not stable (in the Debian sense) at all.

Package management is also very different as it's fundamentally a source based distro, although sometimes the build servers can provide prebuilt packages if they're available. Also, Guix has the concept of "profiles" which group sets of installed packages; typically, there is a system profile as well as a profile for each user, but users can also create their own separate profiles. This means that a user can install packages to their own profile without needing root permissions.

Profile updates are done in an atomic manner, such that changing the set of installed packages (installing, updating, or removing a package) actually creates a new generation of the profile, and it's possible to roll back to a previous generation if something breaks. This is true of the system as well as the user profile(s), of course. A profile generation can also be exported as a manifest, which can then be imported to create a profile generation on another system, allowing package management to be done in a declarative manner.

Finally, Guix has a commitment to ship only free software, and uses linux-libre as its kernel. Debian has a clear separation between free and non-free components but does ship non-free software, including firmware blobs, and I believe as of recently the installer provides them by default. There are unofficial Guix channels (=repositories) that provide these things.