Is what happened considered a form of usury (riba), where the questioner gave his friend 20 dirhams in exchange for 18 dirhams that the friend paid on his behalf, and he did not ask for the remainder either out of shyness or because it was not available?

This is not usury (riba), as there is no condition for increasing the amount. The excess over the debt is considered a gift or a good repayment, based on the Prophet's (peace be upon him) saying: "The best among you are those who are best in repaying debts." If you are not donating it, you have the right to claim the excess.

As for giving the creditor twenty [units] so that he takes his due from it, there is no usury in it according to many scholars, because the excess is a trust in the creditor's hand.

It is stated in "Matālib Ūli an-Nuhā" and "Kashshāf al-Qinā‘" that exchanging silver for a dinar, with the dinar's owner taking his right from the silver, is permissible, even if the taking is delayed for differentiation, and the excess is a trust in the creditor's hand.