My understanding -- and I'm pretty sure it's independent of EFDSS -- is much in line with what Malcolm wrote. The important point is that English Country Dancing, as published by Playford and others, was tremendously popular among the 17th-Century English upper-middle and upper classes. It spread to France and was renamed as Malcolm wrote. It came to New England from France, not from England, hence the name used in New England. The thought that "contra" derives from a Romance root meaning "across from" (e.g. Contra Costa county, across the Bay from San Francisco) is plausible but untrue.

That's my understanding, anyway.