The iron which is run off is called pig iron and one of two things happens to it. It is either put into a cupola furnace to make iron suitable for casting into various shapes, or into a basic oxygen or electric arc furnace to make steel. The steel is then made into shapes as we know it such as sheets, rods, bars wires etc. If the shaping is done hot black mild steel results, if it is rolled cold bright drawn mild steel results.
The main function of the cupola is to reduce carbon, sulphur and silicon, producing a hard brittle substance used for casting vices lathe beds and so on.
The main function of the arc and oxygen furnaces is to further reduce carbon to less than 3% so producing mild steel, which is much stronger than iron.
When small quantities of other materials (e.g. tungsten) are added to mild steel they produce alloy steels which are harder and can maintain their hardness even when red hot.