The bacteria in Stability are alive but not active. They exist in a spore form. They can withstand extreme temperatures and do not require food to survive. When you add them to your aquarium they become active due to dilution.
The bacteria that require refrigeration are active. Refrigerating them slows down their life cycle and they require less food when cold. Because they are active they do require food, and that is packaged with them. They also will not survive extreme heat or cold and will die when they run out of food.