The Difference between Humanist, Transitional and Modern Typefaces

Some key-characters for classifying typefaces are a, e, and R.

Humanist (Serifs, Sans, Slab) a’s mostly have an open upper counter and a rather small bowl; the lower half of the e has an open, friendly »mouth«, whereas the eye in the upper half is usually small. R has a diagonal, often long, maybe swashy tail. The uppercase letters are all of different widths, following the proportions of inscriptional Imperial Roman capitals (Capitalis Monumentalis).
If the typeface has contrast the stroke is likely to be thickest north-east and south-west (rotational symmetric, you can draw a diagonal line trough the thinnest parts). In the venetian subclass the e has a diagonal crossbar.
If the typeface has serifs they are bracketed and often asymmetric.

Transitional typefaces have more regular forms. The a and e are rather open, but in general the letters are not as lively and divers as in a humanist face. R has a diagonal tail, the widths of the uppercase are more equal. Stroke contrast is mostly symmetrical to a vertical axis. Serifs are bracketed and also more symmetrical. These typefaces stand inbetween Humanist and Modern, hence the name.

Modern typefaces, like Didones but also Grotesques have rather closed forms of e and a. Caps are of the same widths and more narrow, also the lowercase letters look comparatively alike (b, d, p, q). The R has a more vertical leg [I miss the proper english terms for that].
In the Didone style the stroke contrast is extremely high with a vertical axis, serifs are very thin and not bracketed. There is a subclass with bracketed serifs, like Century for instance, for which we are all still looking for a good name.