Yeah, I’m from Western NC. We had creeks and branches. A branch is smaller than a creek. A creek is smaller than a river. What we call rivers up in the mountains, they call creeks in the flatlands.
I guess a run is what most people would call a stream.
Nothing here has “stream” in the name but we do say we’re “going upstream” from wherever we are.
[but we should say we’re going uprun, I reckon]...:)