Difference Between White Sage and Cooking Sage

Is there a difference between cooking sage and white sage that is burned?

Yes. White sage (Salvia apiana) is used for ceremonial purposes: the dried leaves are burned for ritual cleansing. It is not used for cooking. The main sage species used for cooking, garden sage (Salvia officinalis), and its many varieties are not used the ritual purposes. To confuse things, there is a White Dalmatian Sage which is a variety of Salvia officinalis and is used for cooking.