The 45-70 does refer to the powder charge, and is not relevent only because the modern solid head cartridge case holds less powder than the original balloon head case, so a modern 45-70 cartridge will only hold 60 grains of black powder. A modern 44-40 or 38-40 hold 30 to 35 gr of black. Most people load them today with smokeless, unless they have an older gun, so the smokeless load bears no relation to the black powder weight. However, other designations lo might refer to dates, like the 30-06, referring to the date of adoption by the US Army Ordinance, of 1906. The 30-30 was 30 grains of a smokeless powder. 38-44 was a 38 cartridge desined for a S&W revolver on a 44 frame.
