James Rachels, answered from the texts and cited to the page.
The Equivalence Thesis is the conclusion that there is no moral difference between active and passive euthanasia as such — that the bare difference between killing a patient and letting a patient die does not, in itself, make a difference to the morality of actions concerning life and death. The Bare Difference Argument establishes the conclusion through the Smith/Jones drowning thought experiment: Smith stands to gain a large inheritance and drowns his six-year-old cousin in the bath; Jones stands to gain the same and enters the bathroom planning the same drowning, but sees the child slip and fall face-down in the water and stands by ready to push the head under if necessary while the child drowns "accidentally." Smith killed; Jones let die.123
The cases are exactly alike in motive, foreseeable outcome, and moral reprehensibility. If the bare difference between killing and letting die were itself morally significant, Jones's behavior would be less reprehensible than Smith's; it is not.4 The argument generalizes: the bare difference is not morally significant in itself. Where killing and letting die differ in moral assessment, they differ because of further factors — the actor's motive (personal gain vs humanitarian concern), the victim's situation (healthy child vs terminal patient in unrelievable pain), the consequences for the rest of the world — not because of the bare killing/letting-die distinction.
In medical contexts where humanitarian motivation, the patient's unrelievable suffering, and the patient's request align, the bare difference between active and passive euthanasia carries no moral weight. If passive euthanasia is sometimes permissible — and the AMA's 1973 statement allows that it is — active euthanasia is sometimes permissible too.5
Like Smith, Jones sneaks in planning to drown the child in his bath. However, just as he enters the bathroom Jones sees the child slip, hit his head, and fall face-down in the water. Jones is delighted; he stands by, ready to push the child's head back under if necessary, but it is not necessary. With only a littfe thrashing about, the child drowns all by himself, 'accidentally', as Jones watches and does nothing.The End of Life - Euthanasia and Morality, p. 113
In the first case, Smith stands to gain a large inheritance if anything should happen to his six-year-old cousin. One evening while the child is taking his bath, Smith sneaks into the bathroom, drowns the child, and arranges things so that it will look like an accident. In the second, Jones also stands to gain if anything should happen to his six-year-old cousin.Can Ethics Provide Answers, p. 66
Like Smith, Jones sneaks in planning to drown the child in his bath. However, just as he enters the bathroom Jones sees the child slip, hit his head, and fall face down in the water. Jones is delighted; he stands by, ready to push the child's head back under if it is necessary, but it is not necessary.Ethical Issues Relating to Life and Death (1979) - contains Rachels Euthanasia Killing and Letting Die, pp. 9–10
There are lots of reasons, such as those I have just mentioned, why a particular act of killing may be morally inferior to a particular act of letting die, or vice versa. All I will argue is that, whatever reasons there may be for judging one act worse than another, the bare fact that one is killing, while the other is letting die, is not among them.The End of Life - Euthanasia and Morality, p. 112
If a doctor deliberately let a patient die who was suffering from a routinely curable illness, then he would be to blame for what he did, just as he would be to blame if he had needlessly killed the patient. It would be no defense at all for him to insist that, really, he didn't "do anything" but just stand there. We would all know that he did do something very serious indeed, for he let the patient die.Ethical Issues Relating to Life and Death (1979) - contains Rachels Euthanasia Killing and Letting Die, pp. 8–9
The Equivalence Thesis has been the focus of sustained philosophical attention since the 1975 NEJM publication — defended by Peter Singer, Helga Kuhse, Jeff McMahan, and the bioethics-utilitarian tradition; attacked by Paul Ramsey and the sanctity-of-life Christian tradition; engaged with by Judith Jarvis Thomson on technical grounds; and revisited by the Doctrine-of-Doing-and-Allowing literature (Frances Kamm, Warren Quinn) that argues for a more refined version of the killing/letting-die distinction the Equivalence Thesis denies. The position is firm and was never softened across the authorship: the 1975 NEJM short version, the 1979 Ladd long version, the 1986 End of Life Chapters 7-8, and the 1997 Can Ethics Provide Answers? reprints all carry the same argument with increasing refinement. The contested ground is whether the Smith/Jones cases are genuinely "exactly alike except for the bare difference" (Frances Kamm in particular argues they are not), and whether the philosophical-conceptual analysis of the killing/letting-die distinction reaches into the medical-ethics setting in the way the argument requires. The position defends the analysis as published with engagement of the canonical objections by name.