in japanese 固化 (koka) is more "solidification" or "curing" than hardening. its "making the haki solid". base armament is just your willpower enhancing attack and defense + being able to touch logias, koka is literally forming the haki energy into a solid armor.
the reason why no one is visibly using armament haki pre-timeskip is that haki is "invisible armor" and you need CoO to see it, so it didnt appear until Luffy, the POV character, developed and trained his observation haki. but its very clear just from the name that busoshoku haki and buso koka are a different thing, because buso koka is literally "giving a solid form to your armaments"