5 You will find many other titles of the Holy Ghost besides. Thus He is called the Spirit of Holiness, as it is written, According to the Spirit of Holiness. He is also called the Spirit of adoption, as Paul says, For you received not the spirit of bondage again unto fear, but you received the Spirit of adoption, whereby we cry, Abba, Father. He is also called the Spirit of revelation, as it is written, May give you the Spirit of wisdom and revelation in the knowledge of Him. He is also called the Spirit of promise, as the same Paul says, In whom you also after that you believed, were sealed with the Holy Spirit of promise. He is also called the Spirit of grace, as when he says again, And has done despite to the Spirit of grace. And by many other such-like titles is He named.
And you heard plainly in the foregoing Lecture, that in the Psalms He is called at one time the good Spirit, and at another the princely Spirit; and in Esaias He was styled the Spirit of wisdom and understanding, of counsel, and might, of knowledge, and of godliness, and of the fear of God. By all which Scriptures both those before and those now alleged, it is established, that though the titles of the Holy Ghost be different, He is one and the same; living and subsisting, and always present together with the Father and the Son; not uttered or breathed from the mouth and lips of the Father or the Son, nor dispersed into the air, but having a real substance, Himself speaking, and working, and dispensing, and sanctifying; even as the Economy of salvation which is to usward from the Father and the Son and the Holy Ghost, is inseparable and harmonious and one, as we have also said before.
For I wish you to keep in mind those things which were lately spoken, and to know clearly that there is not one Spirit in the Law and the Prophets, and another in the Gospels and Apostles; but that it is One and the Self-same Holy Spirit, which both in the Old and in the New Testament, spoke the divine Scriptures.
Source: Catechetical Lectures (New Advent)