What is the difference between the Global Mean and the Global Best Fit?

The Global Best Fit is a best fit plane through the pole vectors. This results in a plane which is approximately parallel to the pole vectors, whereas a mean plane is approximately perpendicular to the pole vectors. A best fit plane is typically used for fold analysis, where it is of interest to find a plane which is perpendicular to a fold axis (and therefore parallel to the pole vectors of the folded planes). You can see this if you use the Fold Analysis option in the Tools menu, select a group of poles with the freehand window, and you will notice that the best fit great circle passes through the selected poles.