The terms "folk dance" and "vernacular dance", objectively, mean the same thing. IMHO, either is "correct" as a description of Lindy Hop. However, "vernacular jazz dance" is, in my experience, the label Lindy dancers and scholars choose to apply. Lindy is a "jazz dance" in the sense of Marshall & Jean Stearns' book Jazz Dance: The Story of American Vernacular Dance (a sense that is not well-reflected in the current "Jazz Dance" article on Wikipedia).  - szarka