IIRC didn't J get introduced originally to denote higher service levels for an upgraded business class product? that is, business class premium?
so you had the original business class, which might have just been a separate cordoned off cabin, but essentially just economy seats (this is going way back). once airlines started to improve this, they needed to differentiate, hence class J.
the same applied in some cases to regular first class F, and premium first class which was denoted by P.
not all airlines introduced the same class codes at the same time, and indeed not all airlines used all the ones available.
today, if I see 'C' I generally take it to mean a regional, or short haul full fare offering with little differentiation... for example most European airlines 'business class' within Europe... it's essentially the same seat and leg room, just more flexibility, lounge access and a meal. however in Australia for example, where domestic business class has wider seats, and a big difference in service, that is designated J.
internationlly, when i see the use of J i take it to mean premium long haul products.