I worked as the Lead OS Architect for Jolicloud (Joli OS) for the past few years, and have also done quite a bit of work customizing Chromium OS for other projects. To answer your question, I can definitely say it's the latter for both OSes:
The structure of a web browser based OS is a persistent browser running over stripped-down Linux based OS.
Joli OS and Chrome OS have some similarities in core design, and some key differences between each other and when compared to a more traditional Linux OS. Let me explain :)
Joli OS uses a Ubuntu-based Linux foundation (which supplies the kernel, X.org, user-space drivers, UI, etc) I worked to strip out as much as possible of the Gnome-based UI and local applications, providing as much of the UX as possible through an HTML5 web app interface. So, from the computer's perspective, when Joli OS starts the Kernel kicks in, which loads the system drivers, user-space drivers, and user-space init scripts. These scripts kick off X.org, which load our session manager, which in turn loads a stripped Gnome shell, and then finally Chromium to the http://my.jolicloud.com start page.
Chrome OS is very similar in this design, except a few key differences: First, it uses a Gentoo-based foundation (Google did used to use Ubuntu, but switched away from it in early 2010). Second, after the Kernel, drivers, and X.org start, Chrome itself handles the session manager which actually "logs in" the user. (This step also decrypts the user home directory, and provides other security features.) Furthermore, rather than a Gnome shell, Chrome also handles traditional window-manager system features like wifi configuration, user accounts, and initiating shutdown and suspend events, etc. Finally, a local start page showing the Chrome web apps installed loads alongside the traditional web browser UI.
In summary, the major difference in the structure of Chrome OS is that Chrome itself is fulfilling more and more of the UX tasks that have been traditionally provided by session- and window-managers like Gnome. By doing everything in the browser, and removing local apps entirely (Incidentally, Joli OS strives to maintain legacy local apps) a faster and more efficient boot-up experience can be presented to the user. Additional differences exist through, i.e., Chrome OS modifies the Kernel, drivers, startup-scripts, and X.org itself to work more efficiently to the target hardware that Chrome OS is designed for.
Don't forget that Ubuntu, Gentoo, and even Joli OS are all designed to have one ISO build run on as many hardware variants as possible, but Chrome OS is designed to only run on a very specific hardware profile. This is another major difference: Chrome OS can strip out suppport for the non-target hardware profiles at build time, also resulting in a more efficient UX with a smaller distribution and boot partition.
Hope this helps :)