There actually is a non-RPG book that presents an alternate Earth where Dragons do exist and have their own set of cladistics. Dracopedia: A Guide To Drawing The Dragons of the World. In this book, dragons and their kin belong to the Draco genus.
Here are the members of the Draco genus:
1. Amphiptere (Draco amphipteridae)
2. Arctic Dragon (Draco nimibiaquidae)
3. Asian Dragon (Draco cathaidae)
4. Basilisk (Draco lapisoculidae)
5. Coatyl (Draco quetzalcoatlyidae)
6. Dragon (Draco dracorexidae)
7. Dragonette (Draco volucrisdae)
8. Drake (Draco drakidae)
9. Feydragon (Draco dracimexidae)
10. Hydra (Draco hydridae)
11. Sea Orc (Draco orcadraciforme)
12. Wyrm (Draco ouroboridae)
13. Wyvern (Draco wyvernae)
The humans of this world domesticated the Dragonettes and the Drakes btw.