Why Are Our Psalm Numbers Different from Other Churches?
As mentioned earlier, the book of Psalms is not something actively studied or discussed in many UOCC parishes. Let us learn a little about the Book of Psalms.
What Are Psalms?
As excerpted from Orthodox Wiki and the OCA website.
King David
The Psalter also known as the Psalms, or Psalms of David is the Old Testament book that contains hymns and poems traditionally ascribed to the Holy Prophet and King David, ancestor of our Lord Jesus Christ [from 1000 B.C.. King David, who played the harp, composed many of the verses of the psalms, the origin of which can sometimes be guessed when reading through his life story.]
One modern commentator, Bishop Demetri [Antiochian], in his foreword to Christ in the Psalms, has described the Psalter as a "golden thread [which runs] through the beautiful garment of Orthodox worship." Indeed, the Psalter forms the core of each of the services of the Daily Cycle, the Divine Liturgy, and the other sacramental offices of the Church.
Different Versions of the Psalter
The numbering and the wording of the psalms differ in the different Christian denominations. The Orthodox Church follows the Septuagint version of the psalter and for this reason the numbers, and not seldom, the texts of certain psalms are different in Orthodox service books from what they are in the Bibles which are translated from the Hebrew. [The "Translation of the Seventy" better known as the Septuagint (from the Latin septuaginta or "seventy") originally referred to a 3rd century B.C. translation of the Jewish Torah into Koine Greek.]
For example psalm 50 of the septuagint (used in our prayer books) is psalm 51 of the King James Bible.
The Structure of the Psalter
The Psalter is divided into 20 kathismata. Each kathisma is further divided into three stases. Each stasis contains between one and three chapters. The exception to this is Psalm 118. Due to its great length, this chapter constitutes the entire XVIIth Kathisma.
Meaning of the Psalter
Virtually all states of man’s soul before God are found expressed in the psalms: praising, thanking, blessing, rejoicing, petitioning, repenting, lamenting, questioning and even complaining. Many of the psalms are centered in the cultic rituals of the Jerusalem temple and the Davidic kingship. Others recount God’s saving actions in Israelite history. Still others carry prophetic utterances about events yet to come, particularly those of the messianic age. Thus, for example, we find Christ quoting Psalm 8 in reference to His triumphal entry into Jerusalem; Psalm 110 in reference to his own mysterious divinity; and Psalm 22, when, hanging upon the cross, He cries out with the words of the psalm in which is described His crucifixion and his ultimate salvation of the world (See Mt 21.16, 22.44, 27.46).
In the Orthodox Church all of the psalms are understood as having their deepest and most genuine spiritual meaning in terms of Christ and His mission of eternal salvation. Thus, for example, the psalms which refer to the king are sung in the Church in reference to Christ’s exaltation and glorification at the right hand of God. The psalms which refer to Israel’s deliverance are sung in reference to Christ’s redemption of the whole world. The psalms calling for victory over the enemies in battle refer to the only real Enemy, the devil, and all of his wicked works which Christ has come to destroy. Babylon thus signifies the realm of Satan, and Jerusalem, the eternal Kingdom of God. The psalms which lament the innocent suffering of the righteous are sung as the plea of the Lord Himself and all those with Him who are the “poor and needy” who will rise up to rule the earth on the day of God’s terrible judgment. Thus, the psalter remains forever as the divinely-inspired song book of prayer and worship for all of God’s People, and most especially for those who belong to the Messiah whose words the psalms are in their deepest and most divine significance.