A hospital graveyard in western Austria could contain the remains of up to 220 people killed by the Nazis. More than 75,000 people were killed by the Nazis for having physical or mental disabilities. That is euthanasia, too often deliberately confused with the administration of palliative care or to "switch off " artificial life support. "Those who cannot remember the past are condemned to repeat it". Graveyard´s photo. EFE. Nice place.
I think it really translates as "easy death", usually for the purpose of medical removal from pain by controlled administration of toxic medications, or medicines which put a person or animal "to sleep" from which there is no waking. I doubt the Nazi plan was truly an "easy death". And since it was administered to those who would have normally continued to live, it wasn't done out of "mercy" but to remove "useless mouths" from the society.
I remember watching pieces from a propaganda film they made I think called "The Legacy" on this subject from a documentary. Sick stuff, as usual with the Nazis. Survival of the fittest and soforth. From what I remember though, the churches in Germany put up quite a protest about it that slowed down the practice.
IMHO, the term euthanasia is ambivalent today, applies to the administration of palliative care, even if accelerate the death of the patient, and to assisted suicide. When someone opposes the legalization of assisted suicide (Christian churches) the answer comes in the first meaning. In my personal point of view, voluntary assisted suicide, is the first step to assisted suicide "not so voluntary" suicide. The lack of formal consent requirement to the administration of palliative care is NOW the way to that first step. The Nazis went up to eugenics, as Mr Formerjughead written. The good news is that will lower the costs of our public, and expensive medical care. (trying to be ironic).