It is important to know the difference. But I think you're wrong on this point, but only on a technicality. Wii is getting both software AND firmware updated, because the Wii is a rare case where you have software that is loaded in firmware. If this were purely a software update, people would be able to wipe the software layer when this error code situation started, and boot from the original image. That you are unable to do that suggests that this is firmware that we're dealing with.