ISTR that the flatiron was the first version of the iron, the box iron, which was taller cos it had a box that you put charcoal in, came in later. So, flat thing that you stuck into the fire to heat up, compared to tall boxy thing - "still using a flatiron Deirdre? I've got a box iron now, stays hot so much longer" etc etc?

Could be wrong. I never iron anything.