Are planes and parallel and belong to the same set?
No, they intersect. Miller index (201) means that your plane intersect basis axis i,j,k on coordinates 2 on i, goes parallel to j and intersect k on coordinates 1. They will look like that:
No, they intersect. Miller index (201) means that your plane intersect basis axis i,j,k on coordinates 2 on i, goes parallel to j and intersect k on coordinates 1. They will look like that: