Destroyed by battle specifically refers to a monster getting destroyed when attacking or being attacked. Generally, when a monster with lower ATK points while in Attack Position or DEF points while in Defense Position battles another monster, that card is destroyed, respectively. However, when a monster battles another monster with an equal ATK, both monsters are destroyed, but battling a monster in Defense Position will end with no destruction on both side. The monster is determined Destroyed as a Result of Battle during the Damage Step.
Many effect requirements can be fulfilled when a monster is Destroyed this way, an example being "Skyscraper 2 - Hero City".
If a monster Destroys its opposing monster during Battle with an effect, the card is not Destroyed as a Result of Battle. Examples are "Mystic Swordsman LV2", "Mystic Swordsman LV4", "Mystic Swordsman LV6" , "Drillroid" and "Ninja Grandmaster Sasuke".