Regarding Brians post, thats the basic difference: Flying on a PPL at a parachuting club with sport jumpers and students only.
The conflict occurs when parachuting BUSINESSES, who sell parachute jumps and training, charge members of the public and are willing to pay their packers, jumpmasters, photographers and make a profit from their BUSINESS.
But they don't pay their pilots because they are allowed to operate aircraft on private ops without commercial pilots. Frankly it makes business sense but is still a cop out and unfair.
If commercial parachuting was recognised as such and required an AOC then much of the problem would be solved (though not all- there's always a few about).