Is Ubuntu a suitable distro for using inside a Docker container? If so, how does the Ubuntu installed by
docker pull ubuntu
differ from Ubuntu 14.04?
Core's page on Ubuntu Wiki explicitly states it is suitable for use in Docker (emphasis mine):
Ubuntu Core is a minimal rootfs for use in the creation of custom images for specific needs. Ubuntu Core strives to create a suitable minimal environment for use in Board Support Packages, constrained or integrated environments, as the basis for application demonstration images, or Linux containers such as LXC or Docker.
The manifest file contains the list of pre-installed packages. Of course, you can install any package available in the Ubuntu repos, but you may have a hard time trying to run GUI applications inside a container.