Public honour requires a witness and external relationships. [definitional]
But there is also that other kind of honour which derives from Aristotle's account in the Nichomachean Ethics of 7.un (book 1, chapter V, 5). This is public, in that it requires a witness, and thus implies a relationship between two or more parties and with persons outside the kin group.
XREF: Connects to Aristotle's Nicomachean Ethics, specifically the distinction between honour that depends on public recognition versus internalized forms of esteem.
Diego Gambetta, Trust - Making and Breaking…, loc. 1788