The first I describe in the last post. The second isn't called an Armed Services Edition but has the Reader's League as publisher. The third is described as "Special edition for free distribution to members of the armed services by the American Red Cross" and looks like the regular ASE edition.
Here is an example of each of the first and second types.
Reader's League "The Pocket Book of Boners", nn, nd
Reader's League "The Pocket Book of Boners", back
Reader's Legue "Red Harvest", nn, nd
Reader's League "Red Harvest", back