rust, corrosion, and oxidation are different terms, and they are related to the same phenomenon. As mentioned, rust is usually related to oxidation of iron and other ferrous metal. Oxidation is looking at it in the point of view of chemisdtry, and is of the most general of all three. Corrosion is a physical-chemical type of deal. You can have other physical process that is visible such as piting, staining, bio-fouling, among others.
Sometimes the oxidated metal can be useful. If I understand FragMaster correctly, he mentioned the formation of protective., oxidated layer. For example, titanium and aluminum is very reactive metal, and without this oxidated layer, it can figuratively "burn" in air.