My “Random House Dictionary of the English Language” includes this definition:
euthanasia: the act of putting to death painlessly a person suffering from an incurable and painful disease or condition.
From now on, we’ll adhere to that definition when discussing animals, i.e. animals put to death painlessly when suffering from an incurable and painful disease or condition will be referred to as “euthanized.”
Animals put to death when not suffering from an incurable and painful condition will be referred to as “killed.”