A finisher pig is this.....
Grower, a pig between weaning and sale or transfer to the breeding herd, sold for slaughter or killed for rations Finisher, a grower pig over 70 kg (150 lb) liveweight.
Cull pig would be an older pig or a sow which hasn't performed well, could mean literally any animal maybe which you have too many of or its not perfect for breeding.
Controlled finisher I think it means they have been recorded from birth weights, weighed reguarlarly and given certain amounts of feed to get to a certain weight on time? Am I right in thinking this?