In contemporary English parlance, to call someone a “man” or “woman of God” substantially means that individual is “godly” or “pious.” As such, the phrase is a descriptor of a person’s moral or religious standing in relation to some perceived measure.
In the Hebrew Bible, however, אישׁ (ה)אלהים ([the] man of God) regularly designates a “prophet.” To be sure, these prophets were often “godly” or “pious,” but even here, there were occasional exceptions to this behavior (e.g., 1 Kgs 13). Rather, when the Hebrew Bible applies this same phrase to David, it fits him into the framework of the broader tradition of the prophet as Yahweh’s representative (Neh 12:24, 36; 2 Chron 8:14). In these particular texts, David’s status as an אישׁ אלהים (man of God) revolves around his plans for the temple’s administration. Even so, scarcely can at least the Davidic psalms be separated from vocation as a royal אישׁ אלהים (man of God).1
1. Cf. 11QPsalmsa 27; Augustine, Civ., 17.14 (NPNF1, 2:352–53).