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.