Jolicloud seems to be the first Cloud OS.
How does it compare to Chrome OS? What's the difference between them? Just mixed local/cloud vs absolutely cloud?
From a more technical standpoint, Jolicloud is a more traditional Linux-based Operating system, and is actually a derivative of Ubuntu. This means that it inherits many things that are part of Ubuntu, such as a package-based build structure using .deb packages. It also inherits items such as the X windowing system. The end result is that though on the surface it may seem more different, under the hood it is much more akin to traditional 'nix systems.
ChromeOS on the other hand is reworking of linux. It is based on the linux kernel, but they have cut out many familiar linux add ons, including the X windowing system, I believe. This means that many user processes are sandboxed into Google's way of doing things which will be through their browser interface, as opposed to the pure linux or ubuntu way of doing things. For example, you won't be able to hack your own python+gtk app and have it run right on ChromeOS, whereas it is much more possible on Jolicloud.
From an applications standpoint, I believe that because google is wrapping everything into its browser, it is actually building replacements for traditional applications whose functionality is lost when they dropped support for X and windowing managers. These are things like file browsers, media players, graphical task management and others. Jolicloud I believe still utilizes many of the built-in applications like nautilus for file management, but they may be adding new applications to further enhance their seamless cloud experience. Of this I am unsure.
To answer your question, you need to define 'absolute cloud' and 'mixed'. I would personally take 'absolute cloud' as being, you log into a cloud-based OS instance over a network connection and your local machine acts as a thin-client.
In this case, neither Chrome OS / Chromium OS or Jolicloud are 'absolute cloud'. They encourage the user to do work in the cloud, but they operate on local executables and everything is processed locally exactly the same as 'regular' operating systems, but with a trimmed down environment.