Kufic script is one of two Arabic scripts that were in use at the beginning of the Islamic era, and was used to write the earliest known Quran manuscripts. It is a square and angular script with specific proportions that are wider than they are high. In addition to its use in the Quran, Kufic script was often used in stone carving and other architectural art. Kufic script became largely obsolete in the 12th century, when it was supplanted by later forms of calligraphy.
Naskhi script is the other Arabic script that dates back to the beginning of the Islamic era. It is a narrower and more rounded script than Kufic, and was used more extensively for letters, documents and other less formal purposes. As it was refined into a more elegant script, it was used more and more often to write the Quran. It did not become obsolete like Kufic script, and forms the basis for many later scripts.
Thuluth is a primarily ornamental Arabic script that was most popular in the medieval era. It is a large, cursive script that was frequently used to decorate mosques as well as for religious and other important inscriptions from the 13th century forward. In Arabic, the word thuluth means "one third," and was likely used to name this script because approximately one third of each letter slopes.
The Diwani script was developed in the late 16th century, at the height of the Ottoman empire, when calligraphy was an especially popular and esteemed art form. It is a particularly ornate script with letters that are joined together in unconventional ways, which makes it more difficult to read than other Arabic scripts. People still use Diwani today as architectural decoration and in some formal documents.
This is the script now commonly used for ordinary handwriting in Arabic, rather than for decorative purposes. It is less ornate than other Arabic scripts and both smaller and easier to write.