"Steel" isn't too inaccurate, with a little bit of luck.
Some compositions, especially stainless steel, can contain much of alloying elements.
But most often - and I expect that from steel wool - steel is pretty much iron. Like 0.5%Si, 0.5%Mn, 0.3%C, rest Fe.
By the way, Mn (comes from Fe ore) and Si (from refractory lining in ovens and melting pots) are so common in steel that most steel designations based on the composition omit them completely, despite their big effect on steel's properties.