The term ‘Drop Scones’ can be rather confusing because it’s used to refer to two distinctly different items. The first usage, which seems to be more common in America, is scones made by the rubbing-in method, just like that described in the Plain Scones recipe but roughly shaped by dropping spoonfuls of the dough onto a baking sheet (as illustrated here).
The second type of ‘Drop Scones’ is not made from dough, but a batter, and its alternative name, ‘Scotch Pancakes’ reveals what it’s most similar to. ‘Drop Scones’ are considered a traditional Scottish recipe, as you can read here.
It’s this pancake variation that grandmother’s recipe below refers to. This is evident from the way the ingredients are combined (straight mixing, no rubbing-in) and the reference to a ‘batter’ that must be left to stand.
Without any clear instructions for the quantity of milk (and I’m not sure how much exactly ’1 Breakfast cupful’ is!), it would certainly help if you were already familiar with working pancake batters to be able to judge the correct consistency by sight. Don’t forget to use self-raising flour or else add some baking powder.
You may wish to compare this recipe with grandma’s Pancake recipe as well as check out some buttermilk variations (buttermilk assists the rise of the batter and tenderises it) here and here. You’ll notice the second recipe substitutes milk+vinegar for buttermilk, you can also use lemon juice,citric acid or cream of tartar to create the same result; read about buttermilk substitutes here.