What is the difference between group and band when applied to assemblages of musicians who play music together?
According to Wikipedia,
A musical ensemble, also known as a music group or musical group, is a group of people who perform instrumental and/or vocal music, with the ensemble typically known by a distinct name.
There’s no absolute difference.
Band originally had closer associations with larger assemblages of musicians (Brass Band, Big Band, etc.). When smaller ensembles became more practical because of new music technology (amplifiers, electric guitars, etc.) mainstream parlance tended to use the term group rather than band.
Group has always remained a bit more ‘mainstream’; it tends to get used more by people outside the music industry, and those who aren’t so interested in the music itself. For example, a TV news item is more likely to refer to U2 as a Group.
Band remains common within the music industry itself, and among devotees of the product. People who listen to U2 are more likely to call them a Band.
Musical ensembles working with many specific ‘genres’ are commonly referred to as bands even in mainstream parlance. For example, this graph shows that Jazz Band is far more common than Jazz Group. But that doesn’t apply to all genres; as this graph shows, Pop Group outweighs Pop Band by a considerable margin.
In short, Band today has a little more ‘street cred’ than Group, even though the actual meaning isn’t really any different.