No, they are not the same thing, but they are both used in cooking. You can also use baking soda in cleaning just about anything, and you can also use baking powder too. You can use baking powder in carpets and scrubbing.
Baking soda is pure sodium bicarbonate. Baking powder on the other hand is a mixture of sodium bicarbonate, an acid salt and an inert substance like corn starch.
Baking powder is used as a leavening agent for baking breads and cakes. When baking powder is added with the other ingredients and placed in the oven, the high temperatures cause the acid salt to break down and the reaction with the sodium bicarbonate releases carbon dioxide. The salt used in the baking powder decides the rate at which carbon dioxide is released and is chosen appropriately to ensure optimum baking.
Baking soda can also be used as a leavening agent if the dish contains acidic ingredients which would break down the sodium bicarbonate and this eliminates the requirement of an acid salt to be added with the bicarbonate. If baking powder were used here, an acidic after taste would be left behind.
They are not the same thing!
Baking soda is sodium bicarbonate, while baking powder is sodium bicarbonate + tartaric acid.
Baking powder is good for making your cakes to rise.
Let's see why is that?
Combinig water and baking powder mixture, the result will be carbonic acid and salt. The carbonic acid is decomposing in water and carbon dioxide gas. The carbon dioxide gas is the "magician" that makes your cake to rise.