According to the current orthodoxy, typefaces—commonly referred to as fonts—come in families. "Font-style" is a formal taxonomic classification; if the W3C consortium had so chosen, the terms could just as easily be "font-relative," like "brainiac sister" or "finagling uncle." Italics themselves are alternate letterforms which may or may not more closely resemble handwriting, are generally slanted, and commonly used for emphasis or specific identification purposes—such as the title of a book in formal English-language scholarship.

You've already made your arguments for Case 1 or Case 2, which is usually the case: more "flexible" language is usually less concise.

Our very own Indra on type classifications.

Btw, why is “ligatures” a tag?

It was an exemple: If a typeface contains ligatures, I should want it to appear in search results for "ligature". Tags are really free in my case.
And thank you for your briliant answer.

Edit — I just read the text you sent Frank. This is really interesting and I must confess, a bit discouraging:

As I am busy with this topic for 14 years now I get really desperate at times. I can understand why my predecessors did not want to continue to bother at some point and why the discussion is preferably avoided at conferences.

In the article the question is always about typefaces, but I am also wondering about how a font weight can modify the drawing of a typeface: How can I know if I am in front of a bold version of a typeface if I don't know anything about its context?
Another question is: Who is supposed to classify the typefaces? In a first time, it will be the type designer himself or the foundry, but users (designers or not) will own more and more tools to organise their fonts and this same people are not supposed to learn complex terminology.
Apologies for my bad english.