Thuluth is the earliest extant style of Arabic calligraphy. Developed in the 7th century, the large, sloping style is still used for ornamental purposes. Thuluth style uses light, long, curving strokes with large curves. Thuluth style is also more likely to feature ornamental marks than other styles, as Thuluth is used almost entirely for ornamental purposes.
The Kufic style developed as a form of formal Arabic script in the 8th century. While it shares a name with the city of Kufah in Iraq, it is not known if there is a connection between the city and the script. The Kufic style is boxy, with round diacritical marks and serifs adorning the consonants. The bold script is well suited to carving into materials like stone or bone, but was also cast in coinage and painted on walls and worked into fabric. The Kufic style became less popular in the 11th century, but is still used on jewelry and computer-generated calligraphy today.
Ibn Muqlah and Ibn al-Bawwab developed the Naskh script in the 10th century. Compared to Kufic script, Naskh script is rendered in thinner strokes with full, deep curves. Compared to Thuluth style, Naskh script has shorter strokes and smaller curves. Diacritical marks appear as dashes and small loops. It was adopted as the chief style for printing Arabic after the advent of the printing press. Naskh script is commonly found in copies of the Quran, and calligraphic decorations for mosques. It is more formal than the Riq'a style, but is still used for Arabic handwriting.
The Riq'a style is the style of Arabic writing you will see in Arabic and Turkish newspapers, books and in Arabic and Turkish handwriting. The Riq'a style is like a shortened version of the Naskh style, with no ornamental marks and curvy letters, but with shorter strokes. You may see a combination of Riq'a and Naskh script in newspapers and books, much as English-language newspapers may have a masthead in an ornate script, but plainer script for the text.
The Ta'liq style developed in present-day Iran between the 9th and 15th centuries. Abd al-Hayy codified the style known for short vertical strokes combined with large horizontal curves and diagonal strokes. Diacritical marks are indicated by dashes, and features a few ornamental marks. Ta'liq style is used for writing Farsi, so it is also known as Farsi style. Ta'liq style is the ornamental style used in Persian and Turkish calligraphy. It was later combined with Naskh to create the Nasta'liq style.
The Diwani script developed during the Ottoman empire during the 15th century. It is an exaggerated cursive style, with no diacritical marks and letters linked in unusual styles. It is a solely ornamental style, as the unusual arrangement of the letters and heavy use of ornamental marks means that even experienced Arabic readers may not be able to discern the proper letter order.