B.M Palmer begins chapter 2 of his great Theology of Prayer by suggesting that the parts of prayer are like the colours of the spectrum: they have a basic unity and merge into each other.  [Unfortunately, the link is currently dead, and I haven’t been able to find an alternative working link]

Adoration and praise are scarcely distinguishable.  Adoration has more to do with God’s nature; praise with his works.  In adoration we view God in himself, as revealed to us in the glorious proportions of his own nature and being; in praise we view him in the operation of his will, displayed piece by piece in what he does.

Adoration, in the Scriptures, often finds expression in the titles by which God is addressed, since these form a rich and accurate impression of his character.  See 2 Thess 3:16; Rom 15:13.

Cf. the following: “The Lord God,” “the Lord our God,” “the Lord God Almighty,” “the great and dreadful God,” “the great and mighty God,” “the Lord strong and mighty,” “the Lord of Hosts,” “the King of glory,” “the Father of glory,” “the Most High,” “the Lord of lords,” “the King of kings,” “the High and Lofty One that inhabiteth eternity,” “thou that dwell-est between the cherubim,” “the Maker of heaven and earth,” “the Lord our shield,” “the Lord our strength,” “the Lord our righteousness,” “the God of hope,” “the God of consolation,” “the God of peace,” “the God of our salvation,” “the Lord God of Abraham, of Isaac, and of Jacob,” “the God of Israel,” “the God and Father of our Lord Jesus Christ,” “the only wise God,” “the blessed and only Potentate,” “the King eternal, immortal and invisible,” “our Father which art in heaven.”

As for the broader expressions of adoring worship, see, for example,

Ex 15:11 – “Who is like unto thee, O Lord, among the gods ? Who is like thee, glorious in holiness, fearful in praises, doing wonders?”

1 Chron 29:10ff. – “Blessed be thou, Lord God of Israel, our Father, forever and ever. Thine, O Lord, is the greatness and the power and the glory and the victory and the majesty: for all that is in the heaven and in the earth is thine; thine is the kingdom, O Lord, and thou art exalted as Head above all. Now therefore, our God, we thank thee and praise thy glorious name”

1 Tim 1:17 – “Now unto the King eternal, immortal, invisible, the only wise God, be power and glory forever and ever. Amen”

1 Tim 6:15f – “Who is the blessed and only Potentate, the King of kings and Lord of lords, who only hath immortality, dwelling in the light which no man can approach unto; whom no man hath seen, nor can see: to whom be honor and power everlasting. Amen”

Jude 25 – “To the only wise God, our Saviour, be glory and majesty and dominion and power, both now and forever. Amen”

‘Jehovah may always be adored, for he is unchangeably worthy of the homage. This, therefore, is a part of prayer independent of the shifting frames by which we are so often painfully embarrassed.’

Adoration has reflexive genefits on the one who prays, by lifting his spirit.

Praise, in comparison, is pitched at a lower key, contemplating the single works of God rather than the totality of his being.  It is correspondingly more enduring, and more easily understood by us.  Examples: Judges 5; 2 Sam 22:2-4; 1 Chron 16:8f; Neh 9:5,7; Psa 9:1; 106:1f; 147:7f; 148:1-5.

Petition and Thanksgiving are correlative: in petition we ask, and in thanksgiving, we thank God, for our blessings.

‘Petition, of course, implies a sense of need awakened in the soul. The want must not only exist, but must be felt.’  But it also implies the recognition of a source of supply.  ‘It is this which distinguishes prayer from an outcry of distress.’  A further presupposition of petition is that there is a warrant for man to approach God and ask.