macstuff 

That is the era that Club bikes are most commonly thought from, it was the innovation in bicycle mechanicals era, but club riding has always gone on and does to this day. The machinery has evolved quite a bit but the reasonings haven't.
I wouldn't want to be the one to put out a controversial definition of a Club Bike, but I think this 30' to 50's era is when it came into its own and the makers acknowledged the following with specially fitted bikes.
Considering we are already in the Vintage bike category, (who is defining vintage?) I'd say defining characteristics of a vintage club machine would be a Lightweight style steel frame, not necessarily panniers but a tail bag, mudguards / fenders, and less than 10 speeds, or some aftermarket contraption that creates 10 or more from the original 1-5 gears.
Consider that Schwinn did make a Continental Clubman model but many of their lightweight bikes were being fitted and used as Club bikes long before that model came out in the early 50's for a year or two. I'm sure half of the Club riders throughout the world had to make their own adequate machine to ride with the boys from town to burg on the weekends.
Oddly enough, I'm not a pack animal and don't really like regular outings like bike rides, motorcycle rides etc. with others, I prefer to ride alone or maybe with one other person. But I do like the Club Bikes and parts.