They're both "immutable" in the sense that they're setting up either read-only Filesystem Hierarchies (as in bazzite, which uses ostree) or Symlinking their entire filesystem hierarchy to a read-only "store" (as in nixos).

Bazzite uses something called ostree to "diff" the filesystem hierarchy much like git does, while Nix basically makes giant read-only store of files and hashes them, then weaves them all together into a "view" of a filesystem that gets symlinked into the context of a running program.