I have never heard of an "exponential scale" as applied to a graph axis, and neither has the internet, other than as a synonym for logarithmic scale!

No, me neither.

if the axis is in exponents then it is an exponential scale. Maybe we should define scale while we are at it.

A logarithmic scale is one in which the evenly spaced marks are consecutive powers (exponents) of 10, rather than consecutive integers. So whereas a linear scale would have the check marks at (say), -1, 0, 1, 2, 3, 4..., a logarithmic scale would have them at (for instance) 10

^{-2}, 10

^{-1}, 10

^{-0}, 10

^{1}, 10

^{2}, 10

^{3}... (or, in other words, 0.01, 0.1, 1, 10, 100, 1000...).

In other words,

**a fixed vertical distance on the logarithmic scale does not represent a fixed numerical amount**: at the bottom of the scale one check mark represents (say) 0.09, whereas at the top of the scale it represents (say) 900. Whereas

**on a linear scale, one check mark represents the same numerical amount** no matter where you are on the scale.