In its broadest sense, corrosion involves the removal of mass from an object. Iron corrodes not because it reacts with oxygen, but because that reaction with oxygen causes flaking and the solid chunk of iron you have gets pits and voids, and eventually disappears altogether into a pile of rust. That is why people say that aluminum doesn't corrode - under the same conditions it reacts just as quickly with oxygen as iron (if not more quickly), but the aluminum oxide forms a tightly bonded passivation layer which blocks further reaction. Since it isn't flaking, no material is being lost, and it is not corroding.
So in a broad sense, it isn't "any reaction with a metal" that is considered corrosion, but "any reaction with a metal that degrades the solid mass of the metal."