Destroying is way of sending cards to the Graveyard.
Cards can be destroyed by card effects, which explicitly use the word "destroy". When a monster is beaten in battle, it is considered destroyed as well.
When a card is destroyed, it is sent to the Graveyard,unless there is a Card on the Field that says otherwise.
Discarding, offering as a Tribute, directly removing a card from play or sending a card to the Graveyard are not the same as destroying a card.
Gameplay and Glossary