I exhort therefore, first of all, that petitions, prayers, intercessions, and givings of thanks, be made for all men:
(31) “Δεήσεις, if we attend to its etymological import, is derived ἀπὸ τοῦ δεῖσθαι, ‘from being in want’ and is a petition for that οὗ δεόμεθα, ‘which we want.’ It is very correctly defined by Gregory Nazianzen in his 15th Iambic Ode: Δέησιν οἵου τὴν αἴτησιν ἐνδεῶν, ‘consider that when you are in want of anything, your petition is δέησις.’ If we attend again to the customary usage of the word, it signifies ‘a petition for a benefit.’ My opinion is, that the various names express one and the same thing, viewed under various aspects. Our prayers are called δεήσεις, so far as by them we declare to God our need; for δέεσθαι is “to be in need.’ They are προσευχαὶ, as they contain our wishes. They are αἰτήματα, as they express petitions and desires. They are ἐντεύξεις, as we are permitted by God to approach Him, not with timidity, but in a familiar manner: for ἐντεύξις is a familiar conversation and interview.” — Witsius on the Lord’s Prayer 