According to the trichotomy of the historical science everywhere in the world known to us, it is suggested that Indian Buddhism can be divided into the periodization of early, medieval, and latter periods.
Generally speaking, the so-called primitive Buddhism, the terminology used in the late nineteenth century, i.e. in the late of Meiji times (1868 A.D.-1912 A.D.), has seldom been used in foreign countries, while recently it still prevails in Taiwan and Mainland China. Perhaps it imports from Japan. But some people think that this terminology has too complex meanings, so had better be abandoned, and the terminology "early Buddhism" should be a good substitute for it. The early Buddhism covers from 5th century B.C. to the middle of the 3th century B.C., i.e. about 150 years to 200 years.
Next, the medieval Buddhism includes both the sectarian Buddhism and the early Mahāyāna Buddhism. The former created śāstras (Abhidharma), and the latter produced many Mahāyāna sūtras and its śāstras. The medieval Buddhism is defined as a period from the middle of 3th century B.C. to early 5th century A.D., about 550 years in total.
Lastly, the period "latter Buddhism" lasts from 320 A.D. to 1203 A.D., about 900 years in total. During that period, the esoteric Buddhism derived from India, and it was destined to disappear as Indian Buddhism came to an end in 1203 A.D. due to the Islamic troops invasion.