I don't think that's quite right. An early name for Steel is Wrought Iron. The Iron had to be wrought, or worked, to remove the impurities. The main one is reducing the carbon content, when the metal is folded it allows the carbon to burn off as carbon dioxide, when the process is repeated often enough you can get the carbon content down to the low single digits. Until the invention of crucible steel this was the only way of producing steel.

Certainly perhaps the Japanese steel may have contained other impurities and been harder to refine but certainly European Iron had to be worked to make Steel.