Corrosion is a natural process, which converts a refined metal to a more chemically stable form, such as its oxide, hydroxide, or sulfide.
Rust is a general term for a series of iron oxides, usually, red oxides, formed by the reaction of iron with oxygen in the presence of water or air moisture.
Rusting is the common term for corrosion of iron and its alloys, such as steel. Many other metals undergo similar corrosion, but the resulting oxides are not commonly called rust.
Rusting is a special term for corrosion of iron.