I'm not certain that I'm asking the right question... but while I have been reading everything docker that I can get my hands on I see that I can install Docker on Ubuntu 12.04 (for example) and then I can install a Fedora container or a different version of ubuntu? (there is an example where the user installed busybox in the container.)
And of course I could be completely wrong.
But it would be my expectation that there was a ephemeral connection between the base system and the container.
restated: what is the relationship between the host OS and the container base image's OS?