Battle damage (戦闘ダメージ, Sentō Damēji) is the damage inflicted to a player's Life Points from battle. Monster Cards can still be destroyed even if battle damage is not inflicted. Damage from direct attacks counts as Battle Damage.
0 battle damage, such as an attack from "Mucus Yolk" with 0 ATK does not cause damage, so no effect can activate in response, including those of "Mucus Yolk" itself and "Gorz the Emissary of Darkness" .
Both words were initially capitalized in card lores, but since Abyss Rising, "battle damage" started being used more frequently. The first time this was used was in the lore of "Drill Synchron", released in Absolute Powerforce.