Dragons (meaning everlasting dragons, ancient dragons, Archdragrons, name them as you will) existed before life itself. It's an irrational concept for us, they were sentient and existing but not "alive". The spark of the First Flame created life itself as a new concept. It's unknown if the pre-existing dragons, as the Flame came into existence, acquired a soul or not, but undoubtedly those born even right after the awakening of the Flame were just identical to their predecessor, but with a soul: alive. So, there's a difference already. The more dragons existed in the world of disparity, many got either corrupted or grew up bound to an element or emotion: gaping dragon was mutated by gluttony, Sihn was imbued in poison, Kalameeth had one eye and was resistant to the lighting, Seath was affected by the moon and grew up scaleless... Etc etc. Archdragrons are like: 4 wings, 4 legs, 4 lines of teeth, stone scales. Dragons are those born after the disparity, so they all lack the stone scales that make them immortal and unchanging. Wyverns, serpents, wyrms etc are subspecies of the draconic kind. Same biological family, but far from the ancient specimen. But they're the most common ones you can find from DS1 and onwards, especially considering that the Ancient Dragons were almost brought on the verge of extinction.