So, yes the brains of people who stutter are different, and yes, in the ways you say- but you can’t assume that the brain differences caused the stuttering. Another theory is that the stuttering itself and the common secondary behaviors along with it (movements, muscle tension, changing pitch or loudness or tone to impact fluency, etc.), and avoidance (thinking around trouble words) actually change the brain and change what areas are activated during speech. Basically in this theory, the brains of people who stutter are more active during speech because they’re during more work than the brain of someone who is doesn’t stutter. The problem is we don’t have any before images of the brains (before they began talking) in any study because how do you choose the “before” babies without knowing who will grow up to be a person who stutters? TL;DR Correlation does not equal causation.