St. Thomas distinguishes between two senses of the end: finis cuius (the end of which or for which), and finis quo (the end by which). The finis quo is the activity by which I attain to an end. For example, eating by which I attain to the end of ice-cream, or knowing by which I attain to the end of knowledge. The finis cuius usually means the end itself that I attain by my activity, for example ice cream, or knowledge. Thus St. Thomas writes:
As the Philosopher says (Phys. ii, 2), the end is twofold—the end for which (cuius) and the end by which (quo); viz., the thing itself in which is found the aspect (ratio) of good, and the use or acquisition of that thing. Thus we say that the end of the movement of a weighty body is either a lower place as thing, or to be in a lower place, as use; and the end of the miser is money as thing, or possession of money as use.
The grammar here might seem a little puzzling. Why is ‘the thing itself’ in which the ratio of good is found indicated by the genitive pronoun, cuius? Why is it not indicated by the accusative, as being the direct object of the activity that attains to it? Why do we not say finis quem, the end which, rather than the end of which? Wouldn’t the finis cuius be more appropriately applied to the one for whom the end is a good? Say I have a person who wants ice-cream. Wouldn’t the most logical way of dividing the end be to say that we have an end by which (eating), an end which (ice-cream), and an end for which (the person)?
In fact, if we look at St. Thomas’s commentary on the passage of Aristotle’s Physics referred to in the quote above we see that there he does use finis cuius to mean the beneficiary of the good:
It must further be noted that we use all things which are made by art as though they exist for us. For we are in a sense the end of all artificial things. And he says ‘in a sense’ because, as is said in first philosophy [Metaph. XII:7], that for the sake of which something comes to be is used in two ways, i.e., ‘of which’ (cuius) and ‘by which’ (quo). Thus the end of a house as ‘of which’ (cuius) is the dweller, as ‘by which’ (quo) it is a dwelling.
What is going on here? I think the key is the remark that he makes at the beginning about art. ‘For we are in a sense the end of all artificial things.’ Here he is considering the products of art as useful or pleasant goods. And useful and pleasant goods are ordered to those who use or enjoy them. That is, the one using or enjoying such a good is really better than the good attained. But when we are talking about the primary case of the good: the honorable good (bonum honestum) we are talking about something that is really loved for its own sake. In loving an honorable good we are not directing it to ourselves—even though we are certainly the beneficiary of it, and we delight in it—but rather we are directing ourselves to it. Thus, a person loves the honorable good of truth not only more than his own knowledge of the truth, but in a sense, more than his very self. He is willing to give his life for the truth. Hence it is fitting to use the genitive finis cuius primarily to refer to the the thing pursued as an end itself. Because it is that which is primarily for the sake of which (cuius causa, or cuius gratia) an action is done. In the case of useful or pleasant goods, the person is himself the primary end, and can be called finis cuius, but in the primary instance of good, it is the good thing pursued that is the true finis cuius for the sake of which all is done.