Welch claims that this term was invented (or at least pioneered) by Tàixū 太虛 in reference to the Wucahng Buddhist Seminary 武昌佛學院 in 1922. He states, "Many of the innovations he (Tàixū) made there proved popular, and by 1945 almost all seminaries in China had become 'institutes for Buddhist studies' in name, if not in substance. To varying degrees they adopted what Tàixū had adopted from lay schools and abroad." (Welch, 107)
Welch lists 72 such seminaries in operation between 1912 and 1950, for which he includes the dates during which they were active. He also includes the average number of monks (or nuns) enrolled. (Welch, 285-287)
Welch estimates, very tentatively, that somewhere on the order of 7,500 Buddhist seminarians graduated in China between 1912 and 1950. Although this estimation is based on incomplete data, it demonstrates that thousands of monks and nuns received their education at Buddhist Seminaries.
(Incomplete) List of Buddhist Seminaries set up by Tàixū (Number in parentheses is Welch's estimate for typical enrollment)
武昌佛學院 1922－ intermittent, ended in 1934, briefly moved to Shanghai in 1937 (70)
龍池佛學院 1927
竹林佛學院 1928-1928
江南九華佛學院 1929－1929
柏林教理院 1930－1931
漢藏教理院 1931-1949 (60-100)
Other Important Seminaries
閩南佛學院 1925-1939 (80) (not founded by Tàixū, but associated with him after 1927)
References:
Pittman, Don A. Toward a Modern Chinese Buddhism: Taixu’s Reforms. (Honolulu: University of Hawai’i Press, 2001), 99.
Shì Dōngchū 釋東初. Zhōngguó fójiào jìndàii shǐ 中國佛教近代史 (A History of Early Contemporary Chinese Buddhism), in Dōngchū lǎorén quánjí 東初老人全集 (Complete Collection of Old Man Dongchu), vols. 1-2. (Taibei: Dongchu, 1974), 2:896.
Welch, Holmes. The Buddhist Revival in China. Cambridge: Harvard University Press, 1968.