Coarse has a wider range and larger steps.
Fine has less range and very small steps. Fine can't go as low in volume as coarse.

The Max Volume is the same.

The reason I offser fine is as you get louder it distorts. Fine gives you very fine control over loudness and distortion. Where coarse may jump from moderately loud and no distortion to loud with distortion in one large step. Where fine allows you to choose a step in between.

Choosing between the two has nothing to do with initvol.