In terms of your "rule of thumb," I like to say that || goes between expressions, and or goes between statements. It's kinda like how , goes between elements, but ; goes between statements. I'm not sure if my phrasing is any more clear to the uninitiated than talking in greek, though.
That's not a good rule though because it doesn't actually provide useful guidance and it makes people think about the operators all wrong. It has nothing to do with expressions or statements. It's all about operators and in which order perl evaluates them. That's the information you need to pass on in your rule so that people can figure out what to do.