I can't speak specifically to North and South Dakota, but having lived in both Arizona and Colorado I can tell you they absolutely are different places cultural

I can't speak specifically to North and South Dakota, but having lived in both Arizona and Colorado I can tell you they absolutely are different places culturally and politically. Speaking to your second point, even in the EU this can be the case. Look at Wallonia and Flanders in Belgium. Spain is also a good example, Catalonia especially.