Discard: When a card gets discarded, it goes to the discard pile of the player whose deck it came from, no matter who played or controlled it. So basically the same thing, only 'destroy' is used on cards where you force another card to be discarded from play.

Is discard the same as sent in Yugioh?

When a card is discarded, it is sent from the field to the Graveyard. However, the opposite is not true. Think of it this way: when you Fusion Summon, the Fusion Summon is treated as a Special Summon. However, when you Special Summon, the Special Summon is NOT treated as a Fusion Summon.

Does discarding count as sending?

a card is considered sent to the graveyard when it moves to the graveyard from the field, deck, hand ,remove from play or extra deck. discard refers only to cards sent from hand to graveyard, and only if at the end of turn because of hand limit, or from an effect that specifically says "discard".