Could you also explain the origins and notable artists that differ them from each other?
There’s not a lot of difference…and yet there is.
Both folk and country come from the same tradition, that of the ballad, story-telling song, with simple accompaniment. As recently as the 1950s trade publications used the terms "folk" and "country" interchangeably. Hank Williams’ 1953 obituaries, for instance, were split about 50/50 between identifying him as a "hillbilly singer" and a "folk singer."
The major differences were that folk music tended to be more event/news-based (think of more modern songs like "The Wreck of the Edmund Fitzgerald" by Gordon Lightfoot) than country music, although country certainly had its share of songs based on events (e.g., Pop Stoneman’s "The Sinking of the Titanic" or the Carter Family’s "Rye Cove"); folk music tended to be more the single "troubadour" singer as opposed to country, which frequently had groups (e.g., the aforementioned Carters, Roy Acuff’s Crazy Tennesseans/Smoky Mountain Boys); and folk music tended to be more political — and left-leaning political — in nature.
Folk had a "split," so to speak, in the mid-60s when Bob Dylan, hailed as the main force behind the "folk revival" of the 60s, "went electric" when the Band backed him. There is now the "folk-rock" (or "contemporary folk," which has its own Grammy category) scene that includes people such as Fairport Convention/Richard Thompson and the Byrds, "folk-country" (again, brought about by Dylan when he recorded "Nashville Skyline") that includes John Prine, the late Steve Goodman, and Gordon Lightfoot, and the "traditional" folk (the single singer with his/her guitar [or autoharp in the case of Bryan Bowers] singer (most of whom don’t get beyond regional success anymore).
Folk’s biggest icons were, and remain, Woody Guthrie, Pete Seeger (and his younger brother, Mike, who passed away last year), the Kingston Trio, Bob Dylan, John Prine, Peter, Paul & Mary, Steve Goodman, and Gordon Lightfoot. People such as Goodman (who wrote "City of New Orleans" and "You Never Even Call Me By My Name") and John Denver (who wrote "Leavin’ on a Jet Plane" for Peter, Paul & Mary) significantly blurred the lines between folk, country, and pop.
The other difference is in the fans. Modern folk fans respect and honor the legends. Modern country fans could care less.