Objection 1. It would seem that a vow consists in nothing but a purpose of the will. According to some [William of Auxerre, Sum. Aur. III, xxviii, qu. 1; Albertus Magnus, Sent. iv, D, 38, "a vow is a conception of a good purpose after a firm deliberation of the mind, whereby a man binds himself before God to do or not to do a certain thing." But the conception of a good purpose and so forth, may consist in a mere movement of the will. Therefore a vow consists in a mere purpose of the will.
Objection 2. Further, the very word vow seems to be derived from "voluntas" [will], for one is said to do a thing "proprio voto" [by one's own vow] when one does it voluntarily. Now to "purpose" is an act of the will, while to "promise" is an act of the reason. Therefore a vow consists in a mere act of the will.
Objection 3. Further, our Lord said (Luke 9:62): "No man putting his hand to the plough, and looking back, is fit for the kingdom of God." Now from the very fact that a man has a purpose of doing good, he puts his hand to the plough. Consequently, if he look back by desisting from his good purpose, he is not fit for the kingdom of God. Therefore by a mere good purpose a man is bound before God, even without making a promise; and consequently it would seem that a vow consists in a mere purpose of the will.
On the contrary, It is written (Ecclesiastes 5:3): "If thou hast vowed anything to God, defer not to pay it, for an unfaithful and foolish promise displeaseth Him." Therefore to vow is to promise, and a vow is a promise.
I answer that, A vow denotes a binding to do or omit some particular thing. Now one man binds himself to another by means of a promise, which is an act of the reason to which faculty it belongs to direct. For just as a man by commanding or praying, directs, in a fashion, what others are to do for him, so by promising he directs what he himself is to do for another. Now a promise between man and man can only be expressed in words or any other outward signs; whereas a promise can be made to God by the mere inward thought, since according to 1 Samuel 16:7, "Man seeth those things that appear, but the Lord beholdeth the heart." Yet we express words outwardly sometimes, either to arouse ourselves, as was stated above with regard to prayer (83, 12), or to call others to witness, so that one may refrain from breaking the vow, not only through fear of God, but also through respect of men. Now a promise is the outcome from a purpose of doing something: and a purpose presupposes deliberation, since it is the act of a deliberate will. Accordingly three things are essential to a vow: the first is deliberation. the second is a purpose of the will; and the third is a promise, wherein is completed the nature of a vow. Sometimes, however, two other things are added as a sort of confirmation of the vow, namely, pronouncement by word of mouth, according to Psalm 65:13, "I will pay Thee my vows which my lips have uttered"; and the witnessing of others. Hence the Master says (Sent. iv, D, 38) that a vow is "the witnessing of a spontaneous promise and ought to be made to God and about things relating to God": although the "witnessing" may strictly refer to the inward protestation.
Reply to Objection 1. The conceiving of a good purpose is not confirmed by the deliberation of the mind, unless the deliberation lead to a promise.
Reply to Objection 2. Man's will moves the reason to promise something relating to things subject to his will, and a vow takes its name from the will forasmuch as it proceeds from the will as first mover.
Reply to Objection 3. He that puts his hand to the plough does something already; while he that merely purposes to do something does nothing so far. When, however, he promises, he already sets about doing, although he does not yet fulfil his promise: even so, he that puts his hand to the plough does not plough yet, nevertheless he stretches out his hand for the purpose of ploughing.
Source: Summa Theologica (New Advent)