The term refining is used in a narrower context.  Henry Corts original puddling process only worked where the raw material was white cast iron, rather than the grey pig iron that was the usual raw material for finery forges.  To use grey pig iron, a preliminary refining process was necessary to remove silicon.  The pig iron was melted in a running out furnace and then run out into a trough.  This process oxidised the silicon to form a slag, which floated on the iron and was removed by lowering a dam at the end of the trough.  The product of this process was a white metal, known as finers metal or refined iron'.