Shell height is the actual height of the shell, plain and simple.
Transformed shell height is a different story. Since most large storage tanks have thicker bottom rings to resist the hydrostatic pressure which get progressively thinner with each shell course, it can be quite difficult to determine what is an allowable shell height to resist wind and vacuum forces. To perform this calculation, each shell course is given a transformed height. This height is the effective height of that course as if it were the same thickness as the thinnest course on the tank. These values are summed for each shell course to determine the transformed height.
For a shell with all courses the same thickness, the transformed height is the same as the actual shell height. For tanks with varying thickness shell courses, the transformed height will always be less than the actual shell height.