"Cook" is a noun, meaning "a person who cooks." It is also a form of the verb "to cook" "Cooking" is a noun, meaning "the act of cooking", as well as another form of the verb "to cook" "Cooker" is a noun, and it's fairly uncommon. It never appears by itself, and is a component word in terms for some machines/tools used to cook specific foods. For example, a "rice cooker" is a machine used to cook rice.

cook is a a "v", means we make sth can be eat cooker is a a "n",means the tools we use it to assist us to cook , like pot ; oven ; can-op ener cooking also a "v"means we are making sth to eat ,we are doing this .