Krdytkyu

In the Wikipedia entry about Anscombe, there is a quote where she juxtaposes traditional utilitarianism to 'consequentialism'.

In what sense are they different and what are some points of divergence (or convergence, if that is actually the case)?

In a nutshell, Anscombe considers utilitarianism to take account, in respect of consequences, solely of the actual consequences of actions. In contrast, consequentialism - a term which she introduced - determines what one should do solely by reference to the foreseen consequences of actions.

The distinction is well brought out in the following extract of a review by Rachael Wiseman :

Teichmann presents Anscombe as making important criticisms of
three central ideas in moral theory: the fact/value distinction; a legalistic
conception of morality; and what he (sic) calls 'consequentialism', the view that
'rational deliberation essentially takes the form of weighing up all the pros
and cons of a possible action or actions and deciding on the action whose
pros most outweigh its cons' (p. 86). (This view is obviously importantly
different from the consequentialism associated with Mill: Millian consequentialism has it that the moral value of an action is a function of its actual
consequences whereas the consequentialism to which Anscombe is opposed
has it that the question 'What should I do?' is to be answered solely by
considering the [foreseen] consequences of one's actions. (Rachael Wiseman, 'Reviewed Work(s): The Philosophy of Elizabeth Anscombe by Roger Teichmann', Mind, Vol. 120, No. 478 (April 2011), pp. 565-570: 567.)

If only foreseen consequences are morally relevant, intended consequences have no separate moral significance. It is no moral justification to say, on the lines of the doctrine of double effect, that although I foresaw that administering pain-relieving medication to a patient would result in her early death, it is morally important that I intended only to relieve pain. I foresaw the early death but I didn't intend it. If I could have avoided it, I would have done so. Consequentialism will have no truck with this distinction - it attaches no separate moral significance to intentions.

Utilitarianism does. An 'old-fashioned Utilitarian' such as JS Mill parts company with the consequentialist. For while Mill allows only actual consequences to determine the morality of an action, he takes intention into account in determining the morality of the agent. For the consequentialist, all that matters are the foreseen consequences of one's actions. There is no place for the morality of the agent - the agent's intentions - as a separate moral consideration.

How does Anscombe combat consequentialism and secure the moral relevance of intentions ?

Against the final thesis, 'consequentialism', Anscombe argues that there is
a morally relevant difference between intended effects and merely foreseen
effects of actions, a difference which consequentialism must deny.
Anscombe's account of intentional action secures this difference by making
it the case that the identity conditions for actions are determined by a
person's answers to the question 'Why?' Intended consequences, but not
foreseen consequences, will feature amongst a person's reasons. (Rachael Wiseman, 'Reviewed Work(s): The Philosophy of Elizabeth Anscombe by Roger Teichmann', Mind, Vol. 120, No. 478 (April 2011), pp. 565-570: 568.)

Terminological note_______________________________________________________

'Utilitarianism' is a term with a wide and heterogeneous range of significance. It is to be noted that Anscombe takes utilitarianism in the form presented by an 'old-fashioned Utilitarian' like JS Mill. It is missing the point to dispute the meaning of 'utilitarianism' with her. She has indicated the sense of 'utilitarianism' with which she is concerned.

Reading___________________________________________________________________

Roger Teichmann, The Philosophy of Elizabeth Anscombe, ISBN 10: 0199603359 / ISBN 13: 9780199603350
Published by OUP Oxford, 2016. See esp. ch.III.

Rachael Wiseman, 'Reviewed Work(s): The Philosophy of Elizabeth Anscombe by Roger Teichmann', Mind, Vol. 120, No. 478 (April 2011), pp. 565-570.

G.E.M. Anscombe, Human Life, Action and Ethics: Essays by G.E.M. Anscombe (St Andrews Studies in Philosophy and Public Affairs), ISBN 10: 1845400615 / ISBN 13: 9781845400613.
See esp. ch. 13, 'Modern Moral Philosophy', first published in Philosophy 53 (1958) : 1-19.

Google's definition of utilitarianism: "The doctrine that actions are right if they are useful or for the benefit of a majority. The doctrine that an action is right insofar as it promotes happiness, and that the greatest happiness of the greatest number should be the guiding principle of conduct."

Google's definition of consequentialism: "The doctrine that the morality of an action is to be judged solely by its consequences."

Both of these moral ideologies values the ends over the means.

Where they differ though is in scope.

Consequentialism makes no presuppositions over what consequences should be the source of an action's judgement. It's just stating a meta-truth relationship between the moral status of an action and the outcome of said action. The only necessary precondition is for the to be a consequence. No consequence, then no moral status for the action which results in the outcome of no consequence. If faced with a dilemma where one of two choices are possible: eternal suffering or non-existence, a consequentialist would choose eternal suffering because non-existence cannot sustain any further consequences.

Utilitarianism does make a presupposition: that happiness/benefit of the majority is the necessary outcome that gives moral status to an action. If faced with the eternal suffering or nonexistence dilemma, a utilitarian would pick non-existence because eternal suffering cannot sustain any further happiness/benefit.

Anscombe must have been focusing on the ends-over-means mindset and disregarding ends-of-ends.