Baking soda is a single compound which has sodium hydrogen carbonate which is alkaline (basic) in nature.
Baking powder is a mixture of sodium hydrogencarbonate and a mild edible(eatable) acid such as tartaric acid. When baking powder mixed with water, then the sodium hydrogen carbonate reacts with tartaric acid to evolve carbon dioxide gas which gets trapped in the wet dough and bubbles out slowly making the cake to rise and hence 'soft and spongy'.The equation which takes place can be shown as:
