There are a lot of subtleties about connotation here. I would say that "storytelling" traditionally primarily meant fiction, but some modern uses also include narrative technique generally, including nonfiction and also marketing. There may also be older traditions of nonfiction storytelling, but that has some connotation of a ritualized or formalized activity (e.g. children sitting in a circle listening to a recitation).
The term that has no connotations of fiction is probably "narrative".
I think many languages have closely related words for fictional narratives and nonfictional narratives.
To me "storytelling" certainly includes true stories, and isn't limited to fiction at all; "narrative" isn't a word I'd use in describing events.
I don't think that's true. Perhaps in your dialect of English, but if I was down the pub and someone started with, "Did I ever tell you the story of when I...", I certainly wouldn't assume it was fictional.