When The British Invasion swept across the U.S., The Beatles, Stones, Dave Clark Five, Animals, Manfred Mann, Gerry & The Pacemakers, Spencer Davis (yup) Group, Yardbirds, Who, Small Faces, etc. etc., were called Groups. The UK press called them Beat Groups. As already mentioned above, Jeff Beck's first solo album was by The Jeff Beck Group.
I have long made the distinction thusly: If a musical ensemble is self-contained (writing the songs, playing the instruments, and doing all the singing), I think of them as a Group. I reserve the nomenclature Band for a musical ensemble which provides musical accompaniment for a singer or group of singers. For example, Frank Sinatra with The Count Basie Band (also sometimes named Orchestra). Frank was also accompanied by The Nelson Riddle Orchestra. In middle and high school, we had both a Band and an Orchestra. The Orchestra included strings and woodwinds, the Band was primarily brass and percussion.
But by the late-60's, the term Band started coming into use in Rock 'n' Roll. While providing accompaniment for Bob Dylan on his 1965-6 world tour, The Hawks were definitely serving as his Band. When their first album was released they became known as The Band (not by their own choosing: contemplating a new name to replace The Hawks, they considered The Crackers or The Honkies. Capitol Records actually chose the name The Band on their own!).
When Rock 'n' Roll criticism became "adult" (In Crawdaddy, Rolling Stone, regional alternative papers), the kids in the suburbs who formed Groups in the wake of The British Invasion---and produced regional and even some national hit singles---became known as Garage Bands. The Chocolate Watchband, The Syndicate Of Sound, People, Stained Glass, The Count Five were all San Jose Garage Bands I saw live in '65 through '68. I even saw Stevie Nicks and Lindsey Buckingham in their San Jose Garage band Fritz (shortened from The Fritz Reiner Memorial Band after receiving a threat from the great conductors estate ;-) .
But as the old expression goes, what's in a name?
