Glad you liked the chocolate cake recipe, wonderful!
Well, all-purpose flour is made from hard wheat and cake flour is made from a combination of hard and soft wheat. So all-purpose has a higher - a 12% gluten/protein content, cake flour about 9-11% and self rising about 7 1/2 to 9%. So basically you want a higher or harder content when you are making bread so that it is strong enough to rise and hold shape. There is also a slight difference in their ability to absorb liquid.
Some Australian recipes, for example, use a combination of flour including the self rising flours. Cake flour generally produces a more crumbly textured cake or a finer grain, which is good for some things, not so good for others.
Yes, it all depends on the recipe and what you are going for.
Sifting the flour will produce more aeration, but won't make it more like a cake flour, just make a lighter flour and make it not pack so much when measured.
Haha, yes we are all second guessing ourselves, haha!
Hugs Squirrelly Cakes