Official repository are a carefully curated set of Docker repositories supported by Docker, Inc.
Automated repositories are Automated Builds that allow you to validate the source and content of an image. Automated Builds automate the building and updating of images from GitHub or Bitbucket, directly on Docker Hub. It works by adding a commit hook to your selected GitHub or Bitbucket repository, triggering a build and update when you push a commit.
In the case of the ubuntu image, there is multiple variants covering Ubuntu 10.04, 12.04, 12.10, 13.04, 13.10 and 14.04. Each variant is identified by a tag and you can refer to a tagged image like so:
REPOSITORY TAG IMAGE ID CREATED SIZE docker-whale latest 1351cae1fdfb About a minute ago 275.1 MB ubuntu latest f753707788c5 7 weeks ago 127.2 MB hello-world latest c54a2cc56cbb 5 months ago 1.848 kB docker/whalesay latest 6b362a9f73eb 18 months ago 247 MB training/webapp latest 6fae60ef3446 19 months ago 348.8 MB