The US Barn Swallow is the same species as most of those seen in Europe, but which are simply called Swallow. They all have the scientific name Hirundo rustica.
But colours can vary somewhat, especially in the underpars with some appearing brilliant white and others looking quite dull or "brownish". Although they can appear to be black & white (or dullish), they are actually deep blue & whatever.
However, perhaps the Swallows that Ken has seen are Cliff Swallows (Petrochelidon pyrrhonota) which breed in much of the US, and Canada. They are slighly smaller than Barn Swallow and generally "brownish" looking to the back and head and lack the tail streamers of the Barn Swallow. In fact, for the occasional sighting in parts of Europe, they might easily be mistaken for Sand Martin or perhaps even House Martin!
Little wonder that artistic impressions vary.
(Most of my bird knowledge is gleaned from hard copies, and pc interactive version, of Birds of the Western Paleartic, backed up with a few internet searches.)