What exactly is Codeberg's relation to Forgejo?

As far as I understand it, Forgejo is a soft-fork of Gitea, and, as far as I am aware, Gitea includes both the backend and frontend. But then I came across Codeberg, which appears to state:

Self-Hosting Forgejo, the software that powers Codeberg.

This makes it sound like Forgejo is the backend, and Codeberg is the frontend, but I'm not 100% sure. If so, did Forgejo separate Gitea's UI, and just soft-fork the backend?