If we have (say) an Adjective phrase classified as a CONSTRUCTION and also as a USAGE, then when we mention an Adjective phrase, we won't know if we are talking about a construction type or a usage type. That's the reason (I believe and agree) that we don't call a phrase such as "A shrewd businessman" as an Adjective phrase (by construction) although its headed by the article/adjective "A". We call it an Absolute phrase, which consists of a noun or nouns and its modifiers (and the only modifiers of a noun are adjectives, because adverbs don't modify nouns).

We don't find the same phrase-type classified under both Construction-type and Usage-type. So, construction types are Absolute/Preposition/Infinitive/Participle. Usage types are Noun/Adjective/Adverb.

Of course, many writers don't follow this distinction; in fact, they don't even talk about two different classifications, construction vs usage. It is a distinction that I practise and I find it useful, logical and practical. The distinction also covers all possibilities, and I believe will withstand any test.