Discarding a card from your Hand can either be as a result of a card effect, or as a requirement to activate a card. Two such examples are "Spirit Reaper" and "Lightning Vortex". When a card is discarded it is not considered destroyed.
Discarding for cards like "Dark Core" or "Lightning Vortex" is considered a Cost. As such, "Dark World" monsters would not get their Special Summon effect.
A card being discarded does not necessarily go to the graveyard. Although this is normally the case, cards like "Macro Cosmos" will send the cards to the Removed from Play Zone instead; however, the card is still considered as being discarded regardless.