Is there a difference between a dove and a pigeon? The short answer is no.
However, Peterson, Mountfort, and Hollom wrote in their 1974 A Field Guide to the Birds of Britain and Europe:
The terms "pigeon" and "dove" are loosely used and interchangeable, but in a general way "pigeon" refers to the larger species with ample, squared or rounded tails, "dove" to the smaller more slender species with longer, graduated tails.
In 1992 the British Ornithologists' Union changed the name of the Rock Dove and Stock Dove to Rock Pigeon and Stock Pigeon, respectively. This unified all the birds in the genus Columba with the name "pigeon." But, then, they also removed New World pigeons formerly in the genus Columba and put them into a new genus called Patagioenas. The American Ornithologists' Union followed suit in 2003.
How does that affect us in the Pacific NW? Well, if you have the "Big Sibley" guide printed in 2000, you will find a listing for "Rock Dove" as Columba livia. You will also find "Band-tailed Pigeon" as Columba fasciata. More recent field guides, such as the National Geographic (5th Edition) will list the new name "Rock Pigeon" still as Columba livia, and "Band-tailed Pigeon" now as Patagioenas fasciata.
Why change the common and scientific names and the order in which they appear on the checklists and field guides? These changes occur as scientists discover new relationships among birds.
That's the party line.
I sometimes joke that this is just a game and the scientists are just making it all up. In a way it's true. People like to pigeon-hole (pardon the pun) things to try to create order out of our complex universe. Nature is rarely so simple.
You may appreciate this blog post from 10,000 Birds:
Requiem for a Rock Dove