On Ubuntu, both.
A system daemon with interesting interactions with avahi-daemon and colord, and a somewhat sandboxed user program, just so Chrome is not overly inconvenienced by its snap sandboxing.
But wait, there is more: The login & lock screen also runs the whole glory of GNOME.. to query printer settings. So you can have those sweet, sweet "new printer" notifications overlaid while inputting your password. Or whatever else "your" printer needs to add there.