I play Mirko Vosk, Mind Drinker as a commander and his ability states that an opponent needs to put cards in their graveyard. Waste Not says when a player discards a card then one of three things happens. My question is in the fine details of what "discard" means: will Mirko trigger Waste Not?
“Discard” specifically means to move a card from your hand to the graveyard:
701.8a To discard a card, move it from its owner’s hand to that player’s graveyard.
Further, MTG cards are very precise with their language. Only an effect that tells you to “discard” a card would count as discarding.
Waste Not's abilities only trigger when a player is instructed to discard a card, period. If the word "discard" was not used, then no card was discarded. If a card is moved from a player's hand to a graveyard by some other means, none of Waste Not's abilities will trigger. If a card is move from a library to a graveyard, they definitely won't trigger.
This is always the case for keywords in Magic. For example, Ob Nixilis, the Hate-Twisted's ability only triggers if the word "draw" was used. It doesn't trigger if a card is otherwise moved from the library to someone's hand, such as with Beast Hunt.
Note that no keyword action or keyword ability corresponds to "move", "put" and "return". Because these terms are not defined in the rules, they use their standard English meaning, and they are therefore synonymous.
Note that no keyword action or keyword ability corresponds to "dies". Any permanent that moves to the graveyard is said to have died.