The specific terminology used is related to the weapons itself, and can be different depending on the system. Dao, for instance, can just mean "blade"… in Japanese, it's pronounced "To"… or, "katana"… which means "sword".
In terms of what makes something a Koryu kata, well, it needs to be a kata that's part of a Koryu (old school). If it's not an old Japanese system (predating the Meiji Restoration), it's not Koryu… and, if it's not from a Koryu, it's not a Koryu kata. I'm not sure why you're asking about Chinese weapons and usage in Japanese arts, though…