I asked for "brown" flour at my bakery and they gave me this but I am not sure if it is whole wheat flour since it isn't white enough like I thought it would be. Is this whole wheat flour or something else, it's also pretty coarse compared to other flours. Any thoughts?
I'm not sure what you mean by "whole wheat" flour. If you truly mean wholemeal flour where all the germ and bran are left in, then it can definitely look this color and texture. The variety of wheat can also influence the color (e.g., harder wheats are sometimes darker).
The term "brown flour" is ambiguous, but I know it can sometimes refer to a ~85% extraction flour (see here and here, for example). 85% extraction means that 15% of the "whole grain" elements are removed (like bran and germ), compared to normal "white flour" which is typically around 70-75% extraction. Such "brown flour" is sometimes referred to as "whole wheat" too, but it's generally lighter in color.
Assuming they gave you wheat flour, my guess is that it's just a higher extraction rate than typical 85% "brown flour" and/or a different wheat variety. If you asked for "whole wheat," they could potentially have given you a 100% extraction (wholemeal) flour, which could definitely be this color.
As for the coarseness, that just depends on the milling. Frequently whole grain flours are milled somewhat coarser (even "stone-milled" in a more traditional manner). Aside from a rustic texture, it's more practical, as finely grinding the bran and germ requires more effort, and it's counterproductive as it causes the flour to become stale faster. (The bran and germ will spoil faster than the endosperm/white flour portion, and increasing surface area through fine grinding will increase the rate of staling.) Also, even in a relatively finely ground whole wheat flour, the rough edges of the bran and germ can make the flour feel coarser, even with a similar particle size.
It may be buckwheat flour, which in my experience looks a lot darker than wheat (even "whole wheat") flour. It also has a nutty or "earthy" smell to it, and a more robust flavor.
(I've never used it for bread, but it make fantastic pancakes!)