Just to add to the abov information from arunmrao, a heat number will identify a unique batch of steel that was produced in a ladle metallurgy furnace. Depending on the steel supplier, this will be ~ 10 tons to over 200 tons. A cast number then identifies where this steel was cast. For steel suppliers that have multiple strand casting, one heat of steel can feed up to 6 casters at the same time. This means 1 heat number would then be divided into 6 different cast numbers.