Cell container size does specify how the internal electrodes are fabricated.
Thin electrodes/more current collector foil layers can supply higher current at lower internal heating than thick electrodes/fewer current collector foil layers designs.
Thin electrode designs take up more internal space for metal foil conductor layers so they yield lower AH's for given volume. Thick electrode design has more of available volume in graphite and LFP electrode material yielding higher capacity, at lower peak current.