I think that rock dove/pigeon, feral pigeon, racing pigeon, homing pigeon all are different names for the same species, just in different degrees of domestication. Second point is that the pure wild rock pigeon without genes from birds that at one time were domestic might not exist (at least in Europe); it seems that after several generations in the wild, most previously domestic birds will revert to a plumage very similar or even identical with the wild form. Unless you see a colony of birds breeding in a mountain/cliff area far away from any town, you should probably not expect it to be a pure wild form; on the other hand, most wild looking birds will be feral enough to count in group C, similar to where you would count a pheasant (if you do).
Cheers
Niels