Typically, a Cloake Board is used for creating your single hive starter/finisher by separating the boxes. You will make your split of the 2 boxes with the CB between with slide in. This way, the old bees go back to the original bottom entrance and the young nurse bees will stay to start the cells when you put in grafts. Once started, you will remove the slide and have a queenright finisher, with bees having free access to move between the excluder to finish cells.
The double screen has two layers of separated mesh which will not allow the colonies to communicate directly but allows air to pass freely. Basically, you are running two separate colonies, by placing a chamber over another with the double screen between. With your new split (assuming from the same hive) above the chamber with the old queen below, the old workers will return to the original entrance. Typically, the double screen is used to 1.) help a weak hive with queen to build, by allowing the conserved heat to rise to the other chamber. 2.) To make a split or introduce a new queen above (again old, less queen-accepting bees go back below), once accepted...the old queen is removed from below and the chambers united with the newly accepted queen from above.
Each is more suited to the specialization I mention. They may be somewhat useful for the other purpose, but not ideal.
Here is a useful Cloake article by Sue Cobey from ABJ that we include with our Cloake Boards for you to download:
A forum community dedicated to beekeeping, bee owners and enthusiasts. Come join the discussion about breeding, honey production, health, behavior, hives, housing, adopting, care, classifieds, and more!