I admit to feeling ambivalent about the classification of typefaces. For that matter the classification of anything. It reminds me of school teachers whose passion has long since dried up, and where all that is left is terminology and dry systems of thought, unapplicable to the world of practice.
It’s a jungle out there. There are so many typefaces that most people will get confused the moment they look at a font menu. What is good, what is bad, what is legible, appropriate to the occasion?
Just to make it even more complicated: Experts don’t agree on systems of classification even. Sure, Sans serifs have their name from the French, and literally means ‘without serifs’. In French they are called Grotesques.
The most widely used typefaces for continous reading in books, particularily fiction, would be termed Oldstyle, which is hopelessly imprecise, as if ‘old’ said anything about their origin at all. Antiqua is the German term, even worse, in a sense; these letters are from the Renaissance, they are not ‘antique’ (from ancient Greek or Roman times), although the Renaissance scholars called them littera antica, because perhaps they reminded them of ancient times.
The Renaissance antiqua is a mixed breed; it is a carolingian minuscule with serifs from the Roman capitals. So its basic shapes are from say, 800 AD, and its detailing is from ca. 100 AD.
Classification helps us to navigate. It points us to the history of letters, if we care to know. It also helps us to see, at best, and may help us to choose correctly.
Note on systems of classification
There are many different systems of classification. Although two categories of letters may be useless, scores of subcategories may be confusing.
The Vox-ATypi system of classification (1954) uses terms like Humanist, Geraldes, Moderns etc. but it may confuse more than illuminate.
Robert Bringhurst (author of Elements of Typographic Style) uses art historical terms to make letters relate to other cultural artefacts, which makes sense; comparing letterforms to buildings of a particular era or style, for example, is helpful. As well as relating letters to paintings or clothes, for that matter.
The classification below, is a hybrid, perhaps overly simplified, but I think it will do as an introduction. More categories may be added later.
Semi sans serifs
Taking form from the writing tool; i.e. broad edged pen, pointed pen, brush etc.
— Batarde / Civilité
— Textura quadrata
In short, I think systems of classification will always fall short , and shouldn’t be taken too seriously