B vent is specifically approved for Category I appliances as regulated by the Nat'l Fuel Gas Code, NFPA54. As such it is for Non-condensing negative pressure vent systems. Stack temp must be 140* above the dew point temp in Cat I.
Cat III is positive pressure, Non condensing, corrosion resistant, 140* above dew point.
The difference is positive/negative pressure. When these Categories were developed an introduced in '92 many furnace manuf gave the option of buying one unit and having it approved for either vertical or horizontal venting, in other words Cat I or III. They quickly found out that the same fan was not going to be happy doing both jobs and pretty much all of them went with either Cat I or Cat III in the non-condensing products. As efficiencies of appliances have increased, B-vent becomes...much shorter lived as opposed to SS. Also, you cannot be blowing flue gases out of the joints of Cat III and you can in I. SS is better and safer.