You pull when you want code from their repo, they pull when they want code from your repo. You don't have permission to push to their repo, so instead you request that they pull from yours.
No you pushed it to your own GitHub repository. So they need to pull from your repository into theirs.
Though I agree the situation is somewhat muddied by the fact that you can create pull requests for branches in the same repository (even though that's not the normal workflow). GitLab's "merge request" terminology is more accurate for that use case.
