I would argue that today, the band not playing for the parents dinner is likely a special band and not the one playing for the graduation.
The existence of two or perhaps even five bands represent bureaucratic band creep.
I don't see how ... if there is more than "one" band per operational unit, it's because they are all really subsets of the larger band. I was a member of the 276th Army Band for several years and was also in the Stage Band, Jazz Band, and Classical Ensemble ... every member of each of those "bands" were already members of the 276th. We were getting paid for being members of the 276th and not one red cent more for performing additionally in these other subsets of the band. We played in those ensembles because we enjoyed the music and there were times when those sorts of performances were appropriate.