Cards put into your graveyard this way are not discarded. Any ability that triggers when you discard a card will not trigger.

If either your graveyard or your hand has no cards in it, the exchange still happens. If one of those zones has any cards in it, you will move them to the other zone.

If you have more cards in hand than your maximum hand size (usually seven) during the cleanup step of your turn, you will need to discard cards down to your maximum hand size.