[git] What are the differences between git remote prune, git prune, git fetch --prune, etc

git remote prune and git fetch --prune do the same thing: deleting the refs to the branches that don't exist on the remote, as you said. The second command connects to the remote and fetches its current branches before pruning.

However it doesn't touch the local branches you have checked out, that you can simply delete with

git branch -d  random_branch_I_want_deleted

Replace -d by -D if the branch is not merged elsewhere

git prune does something different, it purges unreachable objects, those commits that aren't reachable in any branch or tag, and thus not needed anymore.