Euthanasia: it is a medical intervention by which a doctor purposefully ends the life of another person at his or her express and voluntary request.
Assisted suicide: a doctor purposefully helps another person commit suicide or provides another person with the necessary means to that end, at his or her express and voluntary request.
That is induce death or help induce death to a person suffering from an incurable illness in order to shorten his or her suffering and the length of his or her agony.