A "brand" is a name used by a manufacturer of any product. Franco-American is a brand of canned pasta (it happens to be one of several brands Campbell's uses to sell its products).
"Make" is used almost exclusively for cars, and usually in conjunction with the word "model." Ford Taurus, Mitsubishi Eclipse, Toyota Celica--the "make" is the first word in the pair, the "model" the second word. Just as a single company can produce products under several "brands," an automobile company can produce many makes of cars; for example, Ford, Mercury, and Lincoln are all makes produced by Ford Motor Company; General Motors produces Pontiacs, Chevrolets, Saturns, GMCs, among many others.
You would never ask a person "What brand of car do you drive?" You would ask, "What make of car do you drive?" For most other products, you would never ask for them by "make," you would ask for them by "brand."