Do classical authors employ Korgaard's two distinctions? Or do they conflate intrinsic with final, and extrinsic with instrumental?
A passage which seems to give a mixed answer to this question is Plato's Lysis, 218d-220d. There it looks at first as if Plato is clear about the two distinctions; but then he seems to jumble them together.
At first, the distinctions appear to be kept separate:
"Whoever is a friend, is he a friend to someone or not?"Here, to say that something is loved 'for the sake of' (heneka) something seems to mean its being loved as an instrumental good; and to say that it is loved 'on account of' (dia) something seems to mean its being loved as a good the goodness of which is conditional upon something else, viz. as an extrinsic good. E.g. A sick person loves medicine for the sake of health and because of sickness.
"He has to be a friend to someone," he said.
"For the sake of nothing and on account of nothing, or for the sake of something and on account of something?"
"For the sake of something and on account of something." (218d, Lombardo)
But then, famously, Plato seems to blur the two together. Socrates goes on to argue that, if the 'for the sake of' relation were to terminate in a primary object of love, then, since we would not love that thing if we were free from any deficiency or badness, our love for it would be 'for the sake of' badness:
Suppose ... bad were eliminated and could affect no one in body or soul or anything else that we say is neither good nor bad in and of itself. Would the good then be of any use to us, or would it have become useless? For if nothing could still harm us, we would have no need of any assistance, and it would be perfectly clear to us that it was on account of the bad that we prized and loved the good-- ...(220c)Don't the last two sentences of the passage show a conflation? "Take away the enemy and it seems it is no longer a friend" (ei0 de\ to_ e0xqro_n a)pe/lqoi, ou)ke/ti, w(j e1oik', e1sq' h(mi=n fi/lon) suggest as condition. "It was a friend for the sake of an enemy" (fi/lon ga_r h(mi=n a)nefa&nh o2n e0xqrou~ e3neka) suggests an instrument.
... Then that friend of ours, the one which was the terminal point for all the other things that we called 'friends for the sake of another friend', does not resemble them at all. For they are all called friends for the sake of a friend, but the real friend appears to have a nature completely the opposite of this. It has become clear to us that it was a friend for the sake of an enemy. Take away the enemy and it seems it is no longer a friend. (220e--Lombardo)