Yes it means Bright Mild Steel, a cold rolled form of steel stock. Much mild steel it hot formed/rolled/forged etc, this leaves a scale on the material, and it's dimensionally poor. BMS (As we call it here) is simply a better finish, hence 'bright', but only really in comparison.

It is not the same as 'Drill Rod' or Silver Steel', which has added carbon and therefore is harder than MS, and can be heat treated, to greater hardness and toughness. This is usually sold in ground finished sizes, hence also an intrinsically accurate product in it's original state.

I'm not familiar with the term 'Marbrite', but a simple search shows them to be a steel manufacturer. So it's possibly just simply describing flat section material from that maker?