Both coatings are zinc, an element that corrodes much slower than plain steel. The primary difference is that zinc plating is a thin coat (under 1 mil) and galvanizing is a thicker coat (over 1 mil). Zinc is also shinier, as it is often paired with a chromate additive.
Zinc plating is applied most often via an electrical bath. Galvanizing on the other hand is done most often by dipping it in a bath of zinc.
This bath is what gives galvanized material a thicker coating, and it is because of this extra thickness that galvanized parts must be used with one another – the threads are cut to accommodate extra layers of coating. Without that accommodation in thread size, the coating would make the part unable to mate with other, non coated parts.
Galvanized fasteners are more corrosion resistant than zinc plated fasteners. The galvanized coating is thicker and is considered “self healing.” When it is damaged or scratched it is able to fill itself in, protecting the underlying steel. This is not the case for zinc plating. Once a zinc plating is scratched the steel beneath is exposed.