All flour is milled wheat, but you knew that already. However, there are different wheats from different places harvested at different times and they can be (and are) milled differently.
The major difference between cake, pastry, AP, and bread is the amount of glutens, which come from protein. So we differentiate flours by the amount of protein they contain. Looking at the list,
- all purpose; and
the amount of protein increases as you go down the list. However, the amount of protein is not entirely consistent throughout the US -- Southern flours run a tad bit ("tad bit" is a Southern expression, y'all) "softer" (i.e., less protein) than those sold in the rest of the country.
Glutens act as the glue which holds things together. Both their amount and the way they're handled have quite a bit to do with the final structure of whatever it is you baked. Returning to Southern flours by way of illustration, the softness is the reason "southern biscuits" comes out so tender. Southern AP flour (and Bisquick too, for that matter) are the equivalent of Northern pastry flour.
If the question is (and it is), "Which flour to use when?" Then the answer is the annoying, "It depends." One thing it depends on is which flours you happen to have around. You can make an adequate cake with bread flour and vice versa. All of which goes to the great truth: Have your your senses of proportion and humor cleaned and well oiled when you enter the kitchen.
For biscuits: If you don't live in the south, mix cake with AP, 50/50.
For bread: If you live in Alabama, machine mix and knead, and are making an American style roll or white sandwich bread calling for a firm, even crumb, use bread flour -- and preferably a national brand at that; if you live in Chicago, hand mix and knead, and are making a European style, "artisinal" bread which wants an irregular and open structure, use AP.
Returning to the gist of your question: For making cake, everything else being equal, you'll get a softer, better crumb with cake flour than AP.
By the way, you can make faux cake flour, by substituting 2 tbs of corn corn starch for 2 tbs of AP per each cup of flour called for by the recipe. It's not ideal, but better than straight AP if you can't get to the store.
Hope this helps,