Why is the difference from a perfect sphere the same for the Earth and the Moon?
Why is the difference from a perfect sphere the same for the Earth and the Moon?


It isn't, as soon as you look one more digit further.

From NASA's Earth Fact Sheet and Moon Fact Sheet which I found here

                             Moon (km)   Earth (km)      Ratio     (rounded)
Mean radius (volumetric)     1737.4       6371.000      0.27270      0.273
Equatorial radius            1738.1       6378.137      0.27251      0.273
Polar radius                 1736.0       6356.752      0.27310      0.273


If you would like to compare the Moon and Earth parameters further, see the Moon Fact Sheet: