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…
The questions had no relevance to each other but wasn't certain of whether to put it here (since the question involved weapons) yet the second was if there was a word for katas that are not old but maybe it's just that and doesn't have a specific word for it
Kata aren't classified that way, the systems are. If you want a term meaning "modern", go for Gendai (pretty much means "modern")… you could also use "shin" (new) if you wanted…