They direct to the same Wikipedia page which suggests doves are more often slightly smaller but indicates a lack of consistent difference. I had thought there was a stronger distinction...but does anybody here have sources/views on any difference (or equivalence) that may exist between the terms?
Pigeons and Doves are Columbidae of the Columbiformes. Because 'pigeon' and 'dove' are common, not scientific names, which term may be chosen is somewhat variable and interchangable locally and regionally. For example, what is commonly called a 'rock dove' in one area may be called a 'pigeon' in another, or by a different speaker in the same area.
See the Tree of Life page for a fairly exhaustive species listing including in parentheses after the scientific name common names with (frequently) either 'pigeon' or 'dove' attached. Some of the names are linked to photos and descriptions.
The difference between 'pigeons' and 'doves' is, generally, and noting that common usage may not always observe the distinction, what you mentioned: doves are slightly smaller and have pointed tails; pigeons are slightly larger and have rounded tails. In common usage, again, the distinction is also felt to be that pigeons are urban, doves wild; doves are thought to be white, pigeons grey; doves are thought of more as symbols of peace, gentleness and prosperity, while pigeons are thought of more often as flying rats.
Pigeon and dove are common names, not scientific names, just as (for example) American buffalo and mountain goat are. As such, they refer to animals rather haphazardly (and variably) on the basis of popular usage, not genetic similarity and shared ancestry.
There also tends to be considerable inconsistency in the name applied to a particular creature depending on where and when the name is used. For example, the Wikipedia article you cite states that "The species most commonly referred to as 'pigeon' is the feral rock pigeon, common in many cities." And yet Roger Tory Peterson, in his various field guides to North American birds, consistently refers to the "feral rock pigeon" as a "rock dove or domestic pigeon"—even though he identifies the similar-sized and -shaped band-tailed pigeon as a "band-tailed pigeon." (Both were formerly identified as members of the genus Columba and thus considered quite close genetically, though the band-tailed is now listed as belonging to the genus Patagioenas).
In North America, two of the three pigeons with wild populations—the band-tailed pigeon and the red-billed pigeon are native to the Americas, while the rock dove/pigeon is not (all three are relatively large, plump birds). Meanwhile, several members of the Columbidae family native North America and Central America—mourning dove, white-winged dove, white-tipped dove, Inca dove, and ground dove—are normally identified as doves, as are two introduced species—the Eurasian or African ringed turtle dove and the spotted dove from India and Southeast Asia.
For most of North America, the common species are the rock dove/pigeon and the mourning dove. Most people who have a passing familiarity with North American birds will call the former a pigeon and the latter a dove.