Is AA a social club?
Unfortunately, in many cases, yes. A social club is where likeminded people, usually of a similar demographic, gather to pursue common, worldly interests.
How does that differ from fellowship?
We are people who normally would not mix. But there exists among us a fellowship, a friendliness, and an understanding which is indescribably wonderful. We are like the passengers of a great liner the moment after rescue from shipwreck when camaraderie, joyousness and democracy pervade the vessel from steerage to Captain’s table. Unlike the feelings of the ship’s passengers, however, our joy in escape from disaster does not subside as we go our individual ways. The feeling of having shared in a common peril is one element in the powerful cement which binds us. But that in itself would never have held us together as we are now joined.The tremendous fact for every one of us is that we have discovered a common solution. We have a way out on which we can absolutely agree, and upon which we can join in brotherly and harmonious action. This is the great news this book carries to those who suffer from alcoholism. (Big Book, Chapter 2)
What distinguishes fellowship from a social club is firstly the apparent disparate nature of the individuals, and secondly the bond formed by the common problem plus joint action towards the common solution.
In The Lord Of The Rings, the Fellowship Of The Ring is formed of a wizard, a dwarf, an elf, some humans, and some hobbits. Unlikely and divergent companions facing a common peril but with a common goal.