In my understanding feral is a domesticated creature that has found it self adapting back to the wild, while a wild creature was never domesticated at all. How can pigeons be feral?
Wood pigeons are wild and distinctly different from town pigeons.
However, when people say "pigeon" without specifying a particular species, they are almost always referring to feral rock doves (Columba livia domestica) commonly found in urban environments all over the world.