Mild steel is un-alloyed low carbon steel. Carbon steel is iron with only Manganese and silicon as alloying agents...no nickel, chrome , molybdenum, etc, and the ever-present carbon up to around 1.0%max.
Wrought steel designates one which has been hot or cold worked after it's initial casting as opposed to cast steel which is in the form in which it is frozen from the molten state.
