There are some differences between Google Chrome and Chromium. Google Chrome is a closed source project, made by Google. The Chromium project is open source.
Because Chrome is not open source, it does not appear in the Ubuntu repositories, but is available in Google’s 3rd party repositories. Chrome is updated by Google directly, and includes things like Flash and H264 support, by default. However, Flash and H264 support can be installed from the command line.
The packages that install with Google Chrome and do not with Chromium are: chromium-codecs-ffmpeg, chromium-codecs-ffmpeg-extra, flashplugin-installer.
The open source Chromiun project is available in the Ubuntu repos. When updating the software, the Ubuntu developers base their work on the last Chrommium stable version, the version Google Chrome is based of.
Google offers us this table, with differences between Chrome and Chromium.
It is a mather of personal taste, when deciding which one to use, Chrome or Chromium.