It’s a little bit of everything you said. There are numerous observable differences in the structures of those who stutter, specifically in a section called the planum temporale, and in a connective tract called the arcuate fasciculus. It also has an identifiable genetic component, involving several chromosomes. Trauma, too plays a part, and while data on this is harder to come by, researchers and clinicians have noticed that parents reference some sort of life change — a divorce, moving, illness, etc— around the time of stuttering onset enough that asking about such events is standard practice during the client interviews portion of therapy. My professor explained that it’s part genetics, part environment, where someone might carry the genes but not express them until a trauma, like the X-men and the X-gene.