Public IP Address: The cloud servers are automatically assigned an ip address each time they are started. This is an automatic process and the address changes each time the servers are started. There is no option to have a static public ip address.
Host Names: Cloud server hostnames are assigned based on your username and the slot they are in. So the user 'testuser' with a server in slot 2 would have a hostname of testuser2.mylabserver.com. You can connect using the public hostname, however it may not work immediately as DNS can sometimes take a while to propagate.
Private IP Address: The cloud servers each have a private ip address that allows them to communicate to the other cloud servers directly. This is persistent with each server and assigned when the server is created, not started. You can use this ip address and modify the /etc/hosts file to point a hostname to it for use with various services. The details are explained in all lessons where this is required.