cheezz, I use non-fat dry milk powder all of the time in my breads. . .
I add it to the liquid I am using, then proof my yeast in the liquid--when I feel like proofing the yeast. . .
I feel King Arthur specifies their "fine" powdered milk because they want to sell their milk powder. Whirl yours in a blender if you wish to compare. With milk powder, if it is instant milk powder (yes, you can get non-instant milk powder, or you used to be able to get it), finer means that it should dissolve quicker. But I have never had any of the non-fat milk powders I have used fail to dissolve and I do not blenderize them.
I could see where a given amount of fine milk powder might weigh more than regular, coarse milk powder. In that case, if you are using the King Arthur recipe, you could choose to look at the recipe online at the King Arthur site, request measurements to be in weight rather than volume and then use the same weight regular milk powder as the fine milk powder. Hopefully, your recipe is still available on their site, and its page will allow you to ask for weight measures.
Milk or milk powder, for me, gives a slightly richer bread, with finer grain (especially with a standard dough, not a super wet dough) and helps to keep it a little longer at room temperature.