What is the difference between the IP address needed for ssh, and the IP address that is displayed once inside the server

When I ssh into my server, I issue the following command:

ssh <username>@<ip-of-server>

Then, when I get in, I see the following as my prompt:

<username>@ip-<different-ip-address>:

When I try echo $PS1 in the server, then I see the following:

\[\e]0;\u@\h: \w\a\]${debian_chroot:+($debian_chroot)}\u@\h:\w\$, which tells me that the host must be different. Why are these not the same: ip and host?