جَاءَنِي رَجُلٌ عَالِمٌ: the noun and adjective are both indefinite.
جَاءَنِي زَيْدٌ الْفَاضِلُ: Zayd is definite as a proper name, and al-fāḍilu is definite too.
In زَيْدٌ فَاضِلٌ, fāḍilun is normally a predicate, not a direct adjective, since the noun is definite and the predicate is indefinite.
Opening interactive controls...
The Tawābiʿ and Naʿt: Direct and Relational Attributes
جَاءَنِي رَجُلٌ عَالِمٌ: the noun and adjective are both indefinite.
جَاءَنِي زَيْدٌ الْفَاضِلُ: Zayd is definite as a proper name, and al-fāḍilu is definite too.
In زَيْدٌ فَاضِلٌ, fāḍilun is normally a predicate, not a direct adjective, since the noun is definite and the predicate is indefinite.