I think to call it 'industry shorthand' gives it too much legitimacy. It's sloppy language used by some of those who work in the electrical industry - on a par with those builders who talk of a 'yard' or a 'metre' of sand, ballast etc.4mm is electrical industry shorthand for the csa (cross sectional area) of a cable and its measured in square millimeters.
Kind Regards, John.