These oxides become part of the slag. As the iron becomes purer, its melting point rises and it becomes pasty, signaling the time to remove it from the furnace. The slag is then forced out by hammering. Wrought iron created by this process is strong and tough and can be welded and forged. Very popular in the past, it has now been largely supplanted by mild steel.
Steel is a purified alloy of iron with carbon which is manufactured in the liquid state.
The manufacturing process eliminates almost all of the phosphorus, sulfur, and silicon which exist in common cast iron. Medium and high-carbon steels can be hardened and tempered. Reference Pauling Ch. Spin Natural Abund.