"Make" requires a direct object, but "cook" does not. You can say "I am cooking", but if you said "I am making", I would have to ask you "What are you making?" Also, "make" is a far more general word. You can make a building. You can make a bicycle. You can make trouble. You can make friends. You can also make food. But "cooking" is always related to food.

Also, I’d say that I cook something on the stove, bake or roast or broil something in the oven, and make, again, as suggested, a sandwich or salad. I also “make” a meal—dinner or a snack—although you could say, “I’m making carrots for dinner.”

I can cook food. But I can't make food. I think make is in the sense of create.