A single grammatical form of qualification can serve different rhetorical needs. The speaker may clarify a concept, distinguish a known individual, or narrow an indefinite class.
FunctionWhat the qualifier accomplishes
Uncovering meaningExplicates an aspect of the concept
Clarifying a definite referentResolves uncertainty about which known one
Restricting an indefinite termNarrows the range of possible instances
Commentarial terms may be used more broadly in some contexts. The essential question is what work the qualifier performs in this specific utterance.