Rage takes place in the same universe as Fallout.
The Arks were created as a competitor to Vault-Tec's Vaults, which means that Ark people and Vault dwellers are both a sort of stranger to the post-apocalyptic world. As for the difference in apocalypses, it's a result of unreliable stories. Some thought it was a meteor while others thought it was a nuclear war. Feltrite could supposedly be a form of irradiated crystals.