Objection 1. It seems that dulia is not a special virtue distinct from latria. For a gloss on Psalm 7:1, "O Lord my God, in Thee have I put my trust," says: "Lord of all by His power, to Whom dulia is due; God by creation, to Whom we owe latria." Now the virtue directed to God as Lord is not distinct from that which is directed to Him as God. Therefore dulia is not a distinct virtue from latria.
Objection 2. Further, according to the Philosopher (Ethic. viii, 8), "to be loved is like being honored." Now the charity with which we love God is the same as that whereby we love our neighbor. Therefore dulia whereby we honor our neighbor is not a distinct virtue from latria with which we honor God.
Objection 3. Further, the movement whereby one is moved towards an image is the same as the movement whereby one is moved towards the thing represented by the image. Now by dulia we honor a man as being made to the image of God. For it is written of the wicked (Wisdom 2:22-23) that "they esteemed not the honor of holy souls, for God created man incorruptible, and to the image of His own likeness He made him." Therefore dulia is not a distinct virtue from latria whereby God is honored.
On the contrary, Augustine says (De Civ. Dei x), that "the homage due to man, of which the Apostle spoke when he commanded servants to obey their masters and which in Greek is called dulia, is distinct from latria which denotes the homage that consists in the worship of God."
I answer that, According to what has been stated above (Question 101, Article 3), where there are different aspects of that which is due, there must needs be different virtues to render those dues. Now servitude is due to God and to man under different aspects: even as lordship is competent to God and to man under different aspects. For God has absolute and paramount lordship over the creature wholly and singly, which is entirely subject to His power: whereas man partakes of a certain likeness to the divine lordship, forasmuch as he exercises a particular power over some man or creature. Wherefore dulia, which pays due service to a human lord, is a distinct virtue from latria, which pays due service to the lordship of God. It is, moreover, a species of observance, because by observance we honor all those who excel in dignity, while dulia properly speaking is the reverence of servants for their master, dulia being the Greek for servitude.
Reply to Objection 1. Just as religion is called piety by way of excellence, inasmuch as God is our Father by way of excellence, so again latria is called dulia by way of excellence, inasmuch as God is our Lord by way of excellence. Now the creature does not partake of the power to create by reason of which latria is due to God: and so this gloss drew a distinction, by ascribing latria to God in respect of creation, which is not communicated to a creature, but dulia in respect of lordship, which is communicated to a creature.
Reply to Objection 2. The reason why we love our neighbor is God, since that which we love in our neighbor through charity is God alone. Wherefore the charity with which we love God is the same as that with which we love our neighbor. Yet there are other friendships distinct from charity, in respect of the other reasons for which a man is loved. On like manner, since there is one reason for serving God and another for serving man, and for honoring the one or the other, latria and dulia are not the same virtue.
Reply to Objection 3. Movement towards an image as such is referred to the thing represented by the image: yet not every movement towards an image is referred to the image as such, and consequently sometimes the movement to the image differs specifically from the movement to the thing. Accordingly we must reply that the honor or subjection of dulia regards some dignity of a man absolutely. For though, in respect of that dignity, man is made to the image or likeness of God, yet in showing reverence to a person, one does not always refer this to God actually.
Or we may reply that the movement towards an image is, after a fashion, towards the thing, yet the movement towards the thing need not be towards its image. Wherefore reverence paid to a person as the image of God redounds somewhat to God: and yet this differs from the reverence that is paid to God Himself, for this in no way refers to His image.
Source: Summa Theologica (New Advent)