But why would this impact installed drivers or applications? I get this warning "shutting down and starting up again" as different from rebooting from new versions of software, usually.
It's probably because the current state of drivers and applications is also saved along the RAM content I guess. For example, when you install a new driver and it asks you to reboot in order to start working, if you do it manually by shutting down and starting up, it wouldn't have the same effect as restarting, so driver wouldn't start as well. For recent versions of Windows, you need to select restart instead of shutdown-start up to ensure fresh boot-up.