We grind our wheat at home. Many recipes call for "All Purpose Flour" and we have been trying to find how to make our own "All Purpose Flour".
Typical all purpose flour does not include the germ of the wheat, so if you would like to mimic the stuff from the store, you need to grind wheat without the germ (source).
By using hard white wheat and a very fine grind, I have for years made a flour that operates very like whole wheat pastry flour, which can often be substituted for all purpose flour in recipes. To make this same flour suitable for bread I add vital wheat gluten.
All purpose flour is flour that has been milled to achieve a "medium" protein content. So, you need to blend a high protein wheat with a low protein wheat to get flour with a protein content of ~ 9 - 12 %.
It's "all purpose" because you can use it for a variety of recipes. Bread flour is made from high protein wheat and say, cake flour is made from low protein wheat. So, "all purpose" is a middle ground and can be used to make either bread or cake. In general, a hard wheat is high protein and a soft wheat is low protein; so blend the two and you control the protein content.
Anyway the defining factor is the protein content. So if you do this on your own, I would assume that you'd wind up with a whole grain all purpose flour.
For millennia people have made white flour from some ground whole wheat flour. After grinding the wheat blend you choose, you simply use a type of sieve and sift the flour so that only the fine flour falls through leaving the bran in the sieve. This needs to be used right away or properly aged as it will otherwise go rancid. Hope this helps!