The pigeon, overall, gets a bit of a bad rap in terms of its symbolism. For a long time, it’s been linked to disease and referred to as a rat with wings, an undeserved reputation. It also has a reputation of not-so-great intelligence.
Yet when one thinks of a dove, the connotations are completely different: purity, peace, and hope are the traditional values associated with the dove. In truth, pigeon and dove are almost interchangeable labels; all are members of the same Columbidae family, and while smaller species are often called doves and larger ones pigeons, there are no hard rules. The rock pigeon can be just as correctly called a rock dove, and would probably have a far better reputation were this its common label.
One can imagine a Mad Men-esque 1950s meeting where a new soap brand - Dove - is presented: some junior employee raises his hand and says "isn't that just another name for a pigeon?" The client frowns. The meeting is over. The junior employee is given the afternoon to clean out his desk. The scene ends on a shot of the young man exiting the building, few possessions in his hands, as pigeons -- both white and grey -- peck at crumbs in the foreground.