To make it even more confusing, Gitlab hosts their flagship instance as a service at gitlab.com.
So you can do...
Gitlab (self-hosted)
Then there's the Gitea project, which is an open-source thing you can self-host that's supposed to mimic Github's interface. Gitea came under ownership/direction of some for-profit company, so a bunch of faggot tranny communist furry types forked it into Forgejo. codeberg.org is the flagship Forgejo instance, which used to be Gitea until the aforementioned trannies transitioned it.