The Tang Dynasty is often considered the high point of classical Chinese culture, as it was a period of relative stability until the late rebellions. It was strongly influenced by Confucian ideals, and Buddhists were often persecuted.

Dar Al Islam refers, in Islamic cultures and belief, to any nation ruled by Islamic law, Muslims, or where Muslims have security and comfort. In the original interpretation, it was the caliphate of Mohammed and his successors: the Rashidun, Umayyad, and Abbasid states.

In some interpretations, it would refer to any Muslim-majority nation today, from Morocco in the west stretching all the way to Indonesia in the east. In other interpretations, only states ruled by Muslim law qualify, and secular Muslim majority states like Turkey and Indonesia do not. In the interpretations of the most extreme fundamentalists and some groups like ISIS, only they are the caliphate and all others are crusader states run by infidels.

The Tang dynasty was a high point in classical Chinese civilization, lasting from the 7th century until the 10th cent. And by the Dar al Islam we can refer to the Islamic civilization that flourished from the 7th - 13th centuries. This civilization was ruled by Caliphs and can be divided into three periods:

1. the Rashidun (rightly guided) - 7th century

2. The Umayyad Dynasty (ruled from Damascus, 661-750)

3. The Abbasid Dynasty (ruled from Baghdad, 750-1258)

As for some similarities: both were high points in their civilization's histories. In each, literature, sciences, and medicine progressed. Both represent something of a "Golden Age" for their parts of the world.

As for some ways to distinguish these two civilizations: the main distinction is the role of religion. The Dar al Islam was an Islamic civilization, and strived to live up to the ideal set by Muhammad, the Quran, and the early Muslim community. The Tang dynasty adhered to Confucian and Daoist ideals and beliefs - for example, the Tang dynasty used examinations based on Confucian teachings for government posts.

In both, though, there is a tolerance for some other religions. The Islamic civilization was taught to be tolerant of other "People of the Book" (ie. Jews and Christians), and the Chinese Tang dynasty accepted that there were three major faiths: Confucians, Daoists, and Buddhists (although there were periodic persecutions of the Buddhists).

Finally, the Abbasid dynasty fell to Mongol invaders in the 13th. century,  while the Tang dynasty fell to internal rebellions which led to the creation of the Song dynasty. That is, external threats brought down the Abbasids and internal conflict brought down the Tang.