A likely reason: the fish are not affecting the plants directly at all — they are affecting the insects that pollinate them.
Trace the links. Fish eat dragonfly larvae, which live in the water. Dragonflies (the adults) eat flies, bees and butterflies, which live in the air above the pond and visit the flowers around it. So:
Pond B: no fish → dragonfly larvae survive → more dragonflies → fewer bees and butterflies → less pollination → fewer seeds
That is why pond A has a large number of flowering plants around it and pond B has fewer.