I think in a lot of cases when it comes to bands, it really depends on how the group came into being. Were they a bunch of friends who decided to pick up instruments and make music, get popular, etc? Or was it a person putting together a group of musicians to back their work? Does the sound fall apart when you change one or more members? There's a lot of different little things that go toward making that determination.

As to single artists creating and releasing music under a 'band name' I think most of them should probably be considered solo acts.