What if any, is the difference between a band or a group?

A band holds things together. A group is more than one. Got it?

The Mama’s and the Papas weren’t the norm though, were they?

"Got it?" = another know-it-all answer from our resident genius? No wonder first time posters are more than put off.

Spencer Davis Group - 4 musicians.

Just vocalists...it's a group.  If there are musical instruments involved, it's either a band or a group. 

The Jeff Beck Group......isn't The Jeff Beck Band.
The Band....isn't The Group.
Hendrix' Band of Gypsies......isn't Group of Gypsies.
The Allman Brothers Band....isn't The Allman Brothers Group.
Looks to me like names are chosen by how they sound when spoken rather than on other criteria. Personally, I think of a "band" as a "group" of musicians who gather and play on special occasions or in parades; and I think of a "group" as a small collection of performers who perform for entertainment......and money. But I could be wrong.