To discard a card is a form of sending a card from the hand to the Graveyard. Cards can only be discarded by a card that specifically uses this term (as a cost, effect, or as part of a Summoning condition), or during the End Phase due to hand size limit.
A discarded card is normally sent to the Graveyard; however, cards like "Macro Cosmos" will cause any discarded card to be banished instead of going to the Graveyard (although the card is still discarded).
Not all methods of sending cards from the hand to the Graveyard discard; a card must explicitly use the term "discard" for it to do so. Cards like "Hand Destruction", "Chain Destruction", "Polymerization" and "Black Illusion Ritual" can send cards from the hand to the Graveyard, but they do not discard cards.