Taken alone, «غلام» conveys a general description. In «غُلَامُ رَجُلٍ» a relation to some man is added. The annexation supplies information absent from the bare predicate.
Examples:
«زَيْدٌ غُلَامٌ» — Zayd is a servant.
«زَيْدٌ غُلَامُ رَجُلٍ» — Zayd is the servant of a man.
«زَيْدٌ غُلَامُ عَمْرٍو» — Zayd is the servant of ʿAmr, with a named second term.
These assertions differ in the specificity of their information. Annexation matters rhetorically because it adds a relation to the predicate’s meaning, not merely because it has a particular grammatical shape.