Where yeast and sourdough raise bread through biological action, baking soda and baking powder raise breads through chemical action. Baking powder and baking soda produce gas quickly, so no long rise is required. This produces a denser, moister and less open crumb structure than breads risen with yeast or sourdough.
Breads risen with these chemicals are called "quick breads" because they require no rising period but can be baked immediately after they are mixed.
Baking soda is most often bicarbonate of soda, or sodium bicarbonate. When this is mixed with an acid, such as buttermilk, soured milk, orange juice, regular cocoa or sourdough starter, gas is produced.
While quickbreads using sourdough and baking soda are historically significant, they are fairly rare today. They are for most bakers who do this, a way of using up excess starter or starter that has become too acidic.
In this site there are recipes for Sourdough English Muffins, a Carrot Pineapple Cake, and Blueberry Muffins that are risen with baking soda and sourdough starter.
The baking soda will also tend to reduce the characteristic sour taste of a sourdough.
Many quick breads don't contain acids so they are risen with baking powder. Baking powder is a mixture of baking soda and a chemical that produces acid when heated. One of the most common of these chemicals is Alum, or sodium aluminum sulfate.
When baking powders using this chemical are used, some people notice a metallic taste in the baked goods. This seems to be a genetic trait in that some people are very sensitive to the taste, and the sensitivity seems to run in families. Most people do not notice this taste.
The acid caused by heating baking powder reacts with the baking soda to produce gas and raise the quick bread.
A batter mixed with baking soda can typically be held 4 to 6 hours and still bake correctly. A batter mixed with baking powder can be held in a refrigerator for several days without loss of rise. Many bakeries mix enough muffin and cupcake batters at a time to fill several days needs.