When using Organize Boxes, there are three buttons at the top that determine how to move Pokémon, the red (o), blue (o)<->(o) and green -> buttons.
Obviously, the red button is for normal movement and the green one allows you to select multiple Pokémon at the same time. However, I can't for the life of me figure out what the blue button is supposed to do. It seems to do the exact same thing as the red button.
What am I missing?