Objection 1. It would seem that order is improperly defined by the Master (Sent. iv, D, 53), where it is said "Order is a seal of the Church, whereby spiritual power is conferred on the person ordained." For a part should not be described as the genus of the whole. Now the character which is denoted by the seal in a subsequent definition is a part of order, since it is placed in contradistinction with that which is either reality only, or sacrament only, since it is both reality and sacrament. Therefore seal should not be mentioned as the genus of Order.
Objection 2. Further, just as a character is imprinted in the sacrament of order, so is it in the sacrament of Baptism. Now character was not mentioned in the definition of Baptism. Therefore neither should it be mentioned in the definition of Order.
Objection 3. Further, in Baptism there is also given a certain spiritual power to approach the sacraments; and again it is a seal, since it is a sacrament. Therefore this definition is applicable to Baptism; and consequently it is improperly applied to Order.
Objection 4. Further, Order is a kind of relation, and relation is realized in both its terms. Now the terms of the relation of order are the superior and the inferior. Therefore inferiors have order as well as superiors. Yet there is no power of preeminence in them, such as is mentioned here in the definition of Order, as appears from the subsequent explanation (Sent. iv, D, 53), where promotion to power is mentioned. Therefore Order is improperly defined there.
I answer that, The Master's definition of Order applies to Order as a sacrament of the Church. Hence he mentions two things, namely the outward sign, a "kind of seal," i.e. a kind of sign, and the inward effect, "whereby spiritual power," etc.
Reply to Objection 1. Seal stands here, not for the inward character, but for the outward action, which is the sign and cause of inward power; and this is also the sense of character in the other definition. If, however, it be taken for the inward character, the definition would not be unsuitable; because the division of a sacrament into those three things is not a division into integral parts, properly speaking; since what is reality only is not essential to the sacrament, and that which is the sacrament is transitory; while that which is sacrament and reality is said to remain. Wherefore it follows that inward character itself is essentially and principally the sacrament of Order.
Reply to Objection 2. Although in Baptism there is conferred a spiritual power to receive the other sacraments, for which reason it imprints a character, nevertheless this is not its principal effect, but the inward cleansing; wherefore Baptism would be given even though the former motive did not exist. On the other hand, order denotes power principally. Wherefore the character which is a spiritual power is included in the definition of Order, but not in that of Baptism.
Reply to Objection 3. In Baptism there is given a certain spiritual potentiality to receive, and consequently a somewhat passive potentiality. But power properly denotes active potentiality, together with some kind of preeminence. Hence this definition is not applicable to Baptism.
Reply to Objection 4. The word "order" is used in two ways. For sometimes it denotes the relation itself, and thus it is both in the inferior and in the superior, as the objection states; but it is not thus that we use the word here. On the other hand, it denotes the degree which results in the order taken in the first sense. And since the notion of order as relation is observed where we first meet with something higher than another, it follows that this degree of pre-eminence by spiritual power is called Order.
Source: Summa Theologica (New Advent)