In the 1960’s and 70’s, self-contained musical organizations (those that wrote, sang, and played the music on recordings) were called groups, not bands. The term band for many years referred to the musicians who backed up a singer, i.e. (Springsteen’s) The E Street Band and (Tom Petty’s) The Heartbreakers. The Beatles, Stones, Kinks, Yardbirds, Who, Zeppelin, etc. were groups, while Ray Charles, Aretha Franklin, Roy Orbison, Joe Cocker, and more contemporaneously Joan Osborne, Lucinda Williams, Buddy Miller, Emmylou Harris, and other singers had/have a band. Two very different things, their talents assessed very differently.
A musical organization can function in both capacities, as did The Band. The were a great group, but also a great (oy) band. Compare their abilities as a band for Bob Dylan vs. The Dead’s abilities at same. One of them is a MUCH better band in that sense. The Dead may have been, depending on one’s taste, a great group, but they weren’t even close to being a good band. The Dylan & The Dead live album is absolutely unlistenable. IMO, of course. Go ahead, compare it to the Dylan/Band Before The Flood live recordings. A world of difference.
Recording bands are arguably the most talented of them all---just listen to The Swampers, the Muscle Shoals band on the recordings of Aretha, Wilson Pickett, Percy Sledge (the playing on "When A Man Loves A Woman" is musicianship at it’s absolute finest!), The Staple Singers, Steve Winwood, Paul Simon, Rod Stewart, Joe Cocker, Bob Seger, Cat Stevens, Joe Tex, Duane Allman, Boz Scaggs, Glen Frey, J.J. Cale, John Prine, even the damn Rolling Stones, and thousands of others. Another is Booker T & The MG’s, who were also a much better backing band for Dylan than were The Dead. The Heartbreakers also served as Dylan’s band on one tour, with only barely passable results. Another good group/mediocre band.