What if any, is the difference between 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.

No absolute difference, depends how music industry would call them.
G

     A group of pandas is called an embarrassment.  I can vouch for the appropriateness of this name after taking 4 of them to Chucky Cheeses for Elmo's birthday. 
      Three or more geese flocking on the ground is a gaggle; three or more geese flocking in the air are a skein. Here are a few more off the top of my head:

• Cattle: mob or herd
• Cheetas: coalition
• Colts: rag or rake
• Deer: herd or parcel
• Dogs: litter (if they're puppies), pack (if they're wild), or cowardice (if they're curs)
• Dolphins: pod
• Donkeys: pace
• Elephants: herd, parade, or memory
• Elk: gang
• Ferrets: business, hob (male), jill (female), kit (babies)
• Foxes: leash, skulk, or earth (this is the oddest of all group names in my opinion)
• Giraffes: tower
• Gnus: implausibility
• Goats: trip, drove, herd, flock, or tribe
• Gorillas: troop or band
• Hedgehogs: array
• Hippopotamuses: thunder or bloat
• Hyenas: clan or cackle

     Oh, did you mean musical groups and bands?
Sorry,
 Tim

How about this?
A band strongly implies that the members play instruments, aside from just singing and dancing. The Beatles and U2 are examples of bands. A group can be any band. The Beatles and U2 are also groups. But a group can also refer to performers who don’t play instruments onstage (or in a music video). These performers primarily sing and/or dance.