Nothing alike. Steam Deck is running a full Linux distro under the hood, using existing repositories for updates, along with their own launcher (not DE).
Indeed, XBox runs two versions of Windows via a type 1 hypervisor, one version is a minimal Windows kernel tailored for gaming, while the other supports the OS services required to have the UWP runtime running on the same hardware.
Indeed, Steam Deck runs one version of Linux (based on Arch) and enables Windows games through a non-virtualized compatibility layer (Proton, forked from Wine).