Objection 1. It would seem that union is the same as assumption. For relations, as motions, are specified by their termini. Now the term of assumption and union is one and the same, viz. the Divine hypostasis. Therefore it seems that union and assumption are not different.
Objection 2. Further, in the mystery of Incarnation the same thing seems to be what unites and what assumes, and what is united and what is assumed. But union and assumption seem to follow the action and passion of the thing uniting and the united, of the thing assuming and the assumed. Therefore union seems to be the same as assumption.
Objection 3. Further, Damascene says (De Fide Orth. iii, 11): "Union is one thing, incarnation is another; for union demands mere copulation, and leaves unsaid the end of the copulation; but incarnation and humanation determine the end of copulation." But likewise assumption does not determine the end of copulation. Therefore it seems that union is the same as assumption.
On the contrary, The Divine Nature is said to be united, not assumed.
I answer that, As was stated above (Article 7), union implies a certain relation of the Divine Nature and the human, according as they come together in one Person. Now all relations which begin in time are brought about by some change; and change consists in action and passion. Hence the "first" and principal difference between assumption and union must be said to be that union implies the relation: whereas assumption implies the action, whereby someone is said to assume, or the passion, whereby something is said to be assumed. Now from this difference another "second" difference arises, for assumption implies "becoming," whereas union implies "having become," and therefore the thing uniting is said to be united, but the thing assuming is not said to be assumed. For the human nature is taken to be in the terminus of assumption unto the Divine hypostasis when man is spoken of; and hence we can truly say that the Son of God, Who assumes human nature unto Himself, is man. But human nature, considered in itself, i.e. in the abstract, is viewed as assumed; and we do not say the Son of God is human nature. From this same follows a "third" difference, which is that a relation, especially one of equiparance, is no more to one extreme than to the other, whereas action and passion bear themselves differently to the agent and the patient, and to different termini. And hence assumption determines the term whence and the term whither; for assumption means a taking to oneself from another. But union determines none of these things. hence it may be said indifferently that the human nature is united with the Divine, or conversely. But the Divine Nature is not said to be assumed by the human, but conversely, because the human nature is joined to the Divine personality, so that the Divine Person subsists in human nature.
Reply to Objection 1. Union and assumption have not the same relation to the term, but a different relation, as was said above.
Reply to Objection 2. What unites and what assumes are not the same. For whatsoever Person assumes unites, and not conversely. For the Person of the Father united the human nature to the Son, but not to Himself; and hence He is said to unite and not to assume. So likewise the united and the assumed are not identical, for the Divine Nature is said to be united, but not assumed.
Reply to Objection 3. Assumption determines with whom the union is made on the part of the one assuming, inasmuch as assumption means taking unto oneself [ad se sumere, whereas incarnation and humanation (determine with whom the union is made) on the part of the thing assumed, which is flesh or human nature. And thus assumption differs logically both from union and from incarnation or humanation.
Source: Summa Theologica (New Advent)