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

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.

Would groupies be considered a group?

Yeah, the two designations are probably more interchangeable than not. However (!), in spite of the use of the term “group” by even professional ensembles (hah!), I think that “band” tends to carry a little more weight as far as expectations of experience playing together and overall cohesion.  Number of members is generally irrelevant for designation as one or the other.

Then there is the term "boy bands". Were the Monkees an early arranged boy-band group?