Zoro scarred Kaido while having his body fucked up. On the other hand, Luffy was also heavily injured and deals heavy blows to Hybrid Kaido while in base.
It seems like Luffy's CoC is more developed than Zoro's; Zoro only just discovers his CoC based attacks. But Zoro also uses an advanced form, hence Kaido pointed out it will be a scar. Post this battle, Zoro might be able to use it as casually as Luffy for even stronger moves. Maybe this is when ZKK happens.
Is Asura = CoC? I'm not sure tbh. Yes, Asura is a manifestation of his spirit, but it's not like only Conqueror's have a spirit. Zoro being able to manifest Asura doesn't mean Asura expresses CoC yet (in Enies Lobby for example). But now Zoro has awakened his Conqueror's Haki for heavier blows.