Iron oxide is the type of rust with which people are most farmiliar.
Oxidation is a process that naturally occurs with most metals, not just to iron. In simple terms, it is a process where an electron is removed, naturally, in the case of iron. The process, of oxidation and reduction are part of the of a redox reaction.
The iron, used in building construction, will oxide when exposed to moisture and water. Iron is the main component in steel. For this reason it is good to coat structural steel materials with protective protective coatings and applications such application such as hydrability paint or clatting.
The picture below shows an example of failed concrete cracked and broken by expanding oxidized steel reinforcement elements.