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Zinc plated and Galvanized are the same thing. You DO NOT want to use either. The zinc coating will give off toxic fumes when heated, probably not at low smoker temps, and probably not enough to kill you, but I can't guarantee that so why take the chance. Use stainless.
A galvanized coating will burn off, but avoid using anything galvanized on your fire or cooking surfaces. Stainless will last longer and does not rust.