The batteries your talking about are probably SLA and of the AGM **broken link removed** construction.
With liquid Lead acid, the plate size has more to do with capacity and the closer the separation, the higher current can be drawn and the lower ESR. The closer the plates, the more easily damaged by deep discharge.
Take your Carbon Zinc AA, AA, C, D and 9V. Capacity is determined by size. If you do an intuative explanation. The Current/area of the battery plates has to squeeze into to the current/area of the wire. Obviously a larger plate means larger current.