جَاءَ الرَّجُلُ الْعَالِمُ.
“The learned man came.” «الْعَالِمُ» is naʿt: a quality.
جَاءَ أَبُو حَفْصٍ عُمَرُ.
“Abū Ḥafṣ—ʿUmar—came.” «عُمَرُ» is ʿaṭf al-bayān: an identity.
The decisive distinction is the semantic function, not merely a shared case ending.