Yes...Everybody alive knows you make steel with iron and...coal...
Steel is just Iron with a controlled level of carbon and other alloys.
"Iron" is about 70% iron, 25% carbon, and 5% junk.
I'm guessing they use Corundum as an alloy to make the steel more corrosion-resistant and shiny. They also mention it makes it much stronger.
And people
really need to learn the meaning of "Verisimilitude" - Suspension of disbelief.
However, I roll with the "Steel" used in the game, because I (apparently) know more about steel than the OP.
There are many kinds of steel. Apparently, the type used in making weapons and armor in
Skyrim is an Iron/Corundum alloy, giving it the tensile strength, hardness, strength, corrosion-resistance, and elasticity needed to kill dragons. Why Corundum? Because that's the alloy needed to give the Iron the desired qualities. Non-Corundum based steel apparently needs repairs after every fight, if the previous games are anything to go by. If the Smiths in Cyrodiil knew to use Corundum and Iron mixed while still ores, many repair hammers could have been saved.