There is a large range of preferences as to how light, risen a banana bread should be, so there are recipes calling for baking soda and some using baking soda and baking powder. Banana bread batter is rather heavy, so for substantial rising, baking powder will be added. But here's how the strategy works.
Bananas are mildly acid and are the primary source of acidity, unless you use buttermilk or brown sugar. The correct amount of baking soda is the amount that will react with and therefore neutralize the acid in the other ingredients. It is pointless to add more, because it won't do anything, and it will make the batter distinctly alkaline. When greater rising is desired, baking powder is added, because it includes it's own acid sources. It also reserves some rising to happen during baking, thus causing some rising likely to stay risen until fixed by baking. It does that, because some of its acid is released by heat.
We could probably guess which banana bread used baking powder and which used baking soda only.