In my blog Create Working Branch, when run git push origin <non-master>, we actually create a pull request.
More references, it also talks about creating pull request from fork.
I am sometimes confusing about the term, why it is called pull request not push request (because I push my code to remote repo)? And I am not alone, a reasonable explanation see here: Because You are asking the target repository grab your changes, stand on their side it is a pulling operation.
If the changes in local branch develop are ready, but the remote branch develop is out of date, after git pull origin develop your local get messy, you can use git reset --hard roll back to the last commit you made, next delete remote branch on github GUI, then do the git push origin develop to recreate it.