In my limited experience of these things, you need to be really careful with generic ones! When on-board diagnostics started to become popular, most manufacturers had their own codes and the faults could only be read with their own readers. The European Commission wised-up to this and forced them to standardise, so after a particualr date (2006-ish, I think) new types of car started to appear with the same fault codes.
I've tried various generic readers on older cars and they download fault codes, but somtimes they're wrong. For example "P1234" might mean "Lambda sensor open circuit" on a Fiat, but might mean "cam angle sensor short circuit" on a Ford. More recent cars can be read with much more success with generic readers, but if they have some weird feature that's peculiar to that marque and for which an internationally agreed standard fault code hasn't yet been developed, they could still revert to their own - which only ther own equipment could read.