Both works come from his time teaching in Italy from 1265 to 1268. Although the two passages are dealing with different theological questions, when he talks about types of causes he uses the same examples in both of them. Perhaps he was in the habit of using similar examples in his teaching. In this case, the two texts are from about the same time, so it would make sense. Teachers often like to use their favorite comparisons in explaining something. While Thomas did dictate and write, much of his work involved teaching. He was in the classroom all the time, and this developed his theological thought. If we understand him as a teacher, I think we have an important key to his thought. The commentary on Hebrews was given as a lecture and Friar Reginald wrote down the notes.
The two examples involve the bailiff and the king, and the artisan and the hammer. Here are the texts:
From lecture 1, commentary on Hebrews:
“For through Him the Father made the world. But it should be noted that the grammatical object of the preposition ‘by’ or ‘through’ designates the cause of an act: in one way, because it causes a making on the part of the maker. For the making is midway between the maker and the thing made. In this usage the object of ‘by’ can designate the final cause motivating the maker, as an artisan works by gain; or the formal cause, as fire warms by heat; or even the efficient cause, as a bailiff acts through the king. But the Son is not the cause making the Father act through Him in any of these ways any more than He is the cause of His proceeding from the Father. But sometimes the object of ‘by’ designates the cause of the action, taken from the viewpoint of the thing made, as an artisan acts through a hammer; for the hammer is not the cause of the artisan’s action, but it is the cause why an artifact made of iron should proceed from the artisan, i.e., why iron [which the hammer strikes] be worked on by the artisan. This is the way the Son is the cause of things made and the way the Father works through the Son.”
From the Summa, I, q. 36, a. 3
“Whenever one is said to act through another, this preposition "through" points out, in what is covered by it, some cause or principle of that act. But since action is a mean between the agent and the thing done, sometimes that which is covered by the preposition "through" is the cause of the action, as proceeding from the agent; and in that case it is the cause of why the agent acts, whether it be a final cause or a formal cause, whether it be effective or motive. It is a final cause when we say, for instance, that the artisan works through love of gain. It is a formal cause when we say that he works through his art. It is a motive cause when we say that he works through the command of another. Sometimes, however, that which is covered by this preposition "through" is the cause of the action regarded as terminated in the thing done; as, for instance, when we say, the artisan acts through the mallet, for this does not mean that the mallet is the cause why the artisan acts, but that it is the cause why the thing made proceeds from the artisan, and that it has even this effect from the artisan. This is why it is sometimes said that this preposition "through" sometimes denotes direct authority, as when we say, the king works through the bailiff; and sometimes indirect authority, as when we say, the bailiff works through the king.”