There are two important categories in the construction method of a script: regular and running.
The regular construction is the most elemental one. It was developed for books and for optimal reading.
The running script derives from the regular script. It results from faster writing. We can only understand running scripts in contrast with regular scripts.
There is an analogy with Chinese characters. The so-called regular script (楷書 kaishu) is taught in handwriting classes at school and also used as text type in publishing. Running script (行書, xingshu) is usually not taught as it naturally evolves from regular script through speed. And example of regular script on the left and running script on the right.
Formal western writing is based ‘on the use of the broad-nibbed pen’ ‘a broad nib that has a sharp edge and two sharp corners’ (Johnston, 1971 p 127, 71). The angle between the horizontal writing line and the angle of the nibs edge, where the pen writes the thinnest stroke-shape is called the edge angle.
Writing with a sharp broad-nibbed pen makes stroke easier to be pulled towards the writer. Pushed strokes are difficult because the sharp end of the pen tends to go into the paper. It is the edge angle that determines pulled or pushed strokes.
Regular script are characterized by strokes that are exclusively pulled (and not pushed) also called down-strokes.
Running script are characterized by stroke-shapes that are pulled and pushed, also called down-strokes and up-strokes. When the pen does not lift from the paper two or more strokes of regular script become one in running script. Running scripts are often narrow, slanted and the edge angle is slightly higher than in regular script in order to reduce the friction of pushed stroke.
Some handwritten scripts are both regular and running letters (running h and regular u).
Most handwritten books before the typographic press follow the regular construction.