This is getting silly. It is two pollen traps, probably indentical, balanced on top of each other. They are used, one per hive, with the drawer pulled out as shown. The bees land on the draw or fly directly in and climb into the hive through the upper mesh, dropping most of their pollen as they do so. The drawer appears to have a reinforced fine mesh in the bottom of it. It is the reinforcing which makes it look like it has mesh of different sizes. I would guess this larger mesh is a seperate item and simply supports the finer mesh, the purpose of which is to allow air to circulate through the pollen so it doesn't go mouldy. I guess there must be some holes underneath each box or at the rear to allow the air to circulate. Possibly filled with more mesh to stop the bees climbing in.
I would list them simply as pollen traps. I assume for a National Hive. What are the outside dimensions of the boxes? Should be about 18" in which case it would do for a National or Commercial hive.