Hp cartridge id control

I know that many hp cartridges are not interchangeable. I am curious though of some cartridges. I have two hp printers, both use hp 57 color cartridges. The larger black cartridges are different. The psc 1315 uses an hp56 while the f4140 uses an hp54, yet both these use an hp58 in their place for 6 color printing. Is this under hardware control by or is the cartridge use determined by firmware? There is only one CC difference between the two cartridges (54 and 56). I do not like having a logistics nightmare by having more cartridge types than necessary, yet it seems that hp is determined to do this by adding another number to the 270 they already have.