tehillah
Tehillah is simply the noun form of halal. Because it’s used in Psalm 22:3 where God “inhabits the praises (tehillah) of his people,” it is said that this is the praise that God inhabits (as if somehow he doesn’t inhabit regular halal praise.) Others say this word means a spontaneous song, prophetic song, or “song of the Lord.” I can’t see any biblical basis for saying this.
The word simply means “praise.” We praise (verb, halal) with praises (noun, tehillah.)
Mounce's Complete Expository Dictionary of Old and New Testament Words
Noun: תְּהִלָּה (tehillâ), GK 9335 (S 8416), 58x. tehillâ means “praise.” This is the noun related to the verb halāl (GK 2146). The vast majority of the uses of tehillâ are for praise to God. Isaiah specifically states about the Lord God, “I will not give my glory to another or my praise to idols” (Isa. 42:8). Habakkuk announces that God’s “glory covered the heavens and his praise filled the earth” (Hab. 3:3). Because of what God will do for Jerusalem, he will “make her the praise of the earth” (Isa. 62:7; cf. Zeph. 3:20). Other cities and nations will lose the human praise and boasting that has been ascribed to them (Jer. 48:2; 49,25; 51,41).
Understandably, more than half of the occurrences of this word are in the Psalms (which is called in the Heb. by the plural of this noun, tehillîm, “praises, hymns”). Praise belongs to God because of all his “praiseworthy deeds” (Ps. 78:4). Praise awaits God 65:1), and we are instructed to praise him with song 149:1) and with our mouths 34:1; 51,15). The psalmist encourages us to “enter his gates with thanksgiving and his courts with praise” 100:4). In a society in which we seek praise from our fellow human beings, we should never forget the one to whom all praise belongs first and foremost, the Lord our God. “How pleasant and fitting [it is] to praise him” 147:1).