[zozbot234]

> Uh.. nothing about the circle of fifths illustrates anything.

Work it out on music paper, keeping in mind the pattern of whole- and half-steps that defines the diatonic scale. You'll see that it works out. It's not directly illustrated by the circle of fifths, as I point out in a sibling comment. But it works.

The musically-relevant consequence is that you can transpose stuff by separately considering diatonic shifts (depending on the interval you're transposing) and chromatic alterations. It's pretty nifty and intuitive.

> Also it's plain to hear that all those scales have different notes given that they all start on different notes, so clearly they differ by more than just the seventh degree.

Nitpicking, the scales are different in how they assign scale degrees but the sets/collections of pitch classes that define the diatonic scale (hence the key signature) differ by one note as described.