Iʿtirāḍ introduces a separate point within a construction or between closely connected expressions. Tadhyīl follows an assertion with another self-contained clause that supports or generalizes its meaning.
«أَكْرَمْتُهُ ـ رَحِمَهُ اللَّهُ ـ لِعِلْمِهِ»
I honored him—may God have mercy on him—because of his knowledge.
«حَفِظَ الْعَهْدَ. الْوَفَاءُ شِيمَةُ الْكِرَامِ»
He kept his promise. Faithfulness is a trait of honorable people.
The prayer is parenthetical in the first example. In the second, a general maxim reinforces a particular incident.