Specification can mean narrowing a broadly applicable concept; qualification is a wider label for adding a condition or modifier. «Zayd is a learned man» adds a property, but it does not exclusively assign learning to Zayd.
Examples:
«زَيْدٌ رَجُلٌ عَالِمٌ» — Learning is attributed to Zayd.
«زَيْدٌ هُوَ الْعَالِمُ» — Depending on context, the utterance may restrict the predicate to a particular identified party.
The commentary also discusses whether annexation and description are best classed as specifiers or as qualifiers. Either way, the predicate becomes more restricted and informative than it was without those additions.