What is the differences between linear and non linear scales?

On a linear scale, if two pairs of points are the same distance apart, their magnitudes differ by the same amount.

So if distance from point A to B is the same as the distance from point C to D, then

the magnitude of B-A is the same as D-C.

On a non-linear scale this does not apply. On a logarithmic scale, for example,

equal distances, as above would imply that B/A = D/C