Source: Yugioh Wikia
Destroying is a 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, or directly removing a card from play or sending a card to the Graveyard are not the same as destroying a card. For example, if monsters are sent to the graveyard for a Fusion Summon, they are simply referred to as sent to the graveyard. Cards sent to the graveyard for a Synchro Summon are also treated in a similar fashion. However, if "Crush Card Virus" destroys a "Goldd, Wu-Lord of Dark World" in a players hand, its effect won't activate because it is destroyed and not discarded.