Low contrast between thick and thin strokes, vertical or no observable stress 

Grotesque

Medium contrast between thick and thin strokes, slanted stress

Humanist

Low contrast between thick and thin strokes, with vertical stress, and circular round forms

Geometric 

A typeface without a serif, with the word Sans being french for "without". 

Ther are three classifications: grotesque, humanist, geometric

DePaul University

There are five categories of fonts: Serif, Sans Serif, Monospace, Handwriting, and Display. 

Type Classification

Material Design Documentation

Serifs contain protrusions at the beginning and/or end of a stroke of a letter, like an extra piece to the basic letterform. 


There are four classifications under Serif: Old-Style, Transitional, Didone or neoclassical, Slab

Serif

Sans Serif

Monospace

Handwriting fonts imitate a natural handwritten feel. They are often time very expressive and are often used for header fonts.

The three forms include: black letter, script, and handwriting

Handwriting

A combination of all classifications only to be used for headers.

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