Is there a difference between killing a character and discarding it from play?

yes if a character is killed they go into the dead pile and subsequently if they are a unique character noted by having a flag next to their names, it means that you can no longer play any more copies of that character.

If they are discarded they go into your discard pile and for unique characters this means that they can still be played, provided there are no other copies of that character in your dead pile.

The practical result of taking a card that is in play and moving it out of play is the same, but, as Venters says, the two are not equivalent. The primary difference between "kill" and "discard" is where the card is put when removed from play (the dead pile and the discard pile, respectively), which will have consequences, particularly for unique cards. It is also important to remember that "kill" and "discard" are different for saves, responses, and other effects. For example, if a card says, "save a character from being killed," you cannot use it against an effect that says "discard a character."