Both affect young leaves and cause interveinal chlorosis, which explains the persistent confusion. The difference lies in the pattern. Iron deficiency produces a sharp yellow — sometimes almost white — with a fine, highly contrasted network of green veins, like lacework. Manganese deficiency creates a more diffuse pale green veil with blurred edges, often accompanied by small, scattered necrotic spots on the leaf blade.
The second clue is pH. These two elements become unavailable at different points, with iron dropping out first as you approach neutrality. Hydroponics targets a slightly acidic root zone, around 6.0 to 6.5, whereas an aquaponic system settles closer to 6.8 to 7.0 to protect the nitrifying bacteria. It is precisely this deliberate offset that produces your symptoms, and it explains why the same plant would fare better in straight hydroponics.
The third clue is experimental. Correct iron first, then observe only the leaves that emerge afterwards, over two to three weeks. If they come through a good strong green, the diagnosis was correct. If the pale veil and spots persist on those new leaves, look towards manganese — starting by bringing the pH down rather than adding yet another product.