What are Ubuntu cloud images?

One difference between standard images and cloud images is that Ubuntu Cloud Images come with cloud-init

From the first link : "Ubuntu Cloud Images are pre-installed disk images that have been customized by Ubuntu engineering to run on cloud-platforms such as Amazon EC2, Openstack and LXC." So, that's what those are for.

The second link is for their normal distro. If you wanted to install Ubuntu on a physical (or virtual) machine that you are sitting in front of or otherwise have access to and good control of, you would download something from the second link and install it.