To me euthanasia is when the government or others kill those who are disabled, elderly, terminal, or otherwise "felt unneeded" without their consent and against their will. That is what I define as euthanasia and it is also out and out murder.
If a person commits suicide, that's suicide and assisting them in that is also wrong in my book, but does not rise to the horror of true euthanasia.
For me, euthanasia is the killing of another person, under conditions that the killer has justified as being in the victim's best interests, i.e. they have no hope of recovery, etc.
Having the victim's pre-written authorization does not make it right in my book. It is still murder.