Difference between baking soda and baking powder
As LDC3 says, Baking soda is simply sodium bicarbonate, $\ce{NaHCO3}$. When one adds an acid, the following reaction occurs: $\ce{HCO3- + HA -&gt; H2CO3 + A-}$ and the carbonic acid releases carbon dioxide: $\ce{H2CO3 -&gt; CO2 + H2O}$ (these are both equilibrium reactions, but as you can observe when you add vinegar, a lot of gas is produced and the gas is generally lost, pushing the equilibrium towards making carbon dioxide).

Baking powder is a mixture of sodium bicarbonate and one or more weak acids. When dry, no reactions occur, but when wet, the components dissolve and can react. The observed differences when mixing vinegar with baking powder probably result from the fact that there is less sodium bicarbonate in a given volume of baking powder than baking soda, and baking powder often contains starch, which can influence the properties of the added liquid, giving the bubbles a different appearance.