According to the EPI Data Centre Professional (CDCP®) Preparation Guide, Class K fires involve cooking appliances that use combustible cooking media such as vegetable or animal oils and fats (page 28). Class K fires require special extinguishing agents that can suppress the high-temperature flames and prevent re-ignition. Class K fires are different from Class B fires, which involve flammable liquids such as gasoline, oil, or paint.
References:
*EPI Data Centre Professional (CDCP®) Preparation Guide, page 28
*Fire Classes and Extinguishing Agents | The Fire Equipment Manufacturers' Association