There are over 300 pigeon/dove species, and nearly all of these are wild and have never been domesticated.
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.
Wood pigeons are wild and distinctly different from town pigeons.
https://en.m.wikipedia.org/wiki/Common_wood_pigeon