I'm curious about the time of the change from "chairman" to "president" as the English translation for "主席". According to Wikipedia, "The office [of President of the People's Republic of China] was formerly known as the State Chairman and the Chinese Zhǔxí still literally translates to this. The official translation switched to President after 1982 in conformity with Western terminology, although the Chinese word is still used to translate other offices of 'chairman'". So the change occurred in 1982. What's special about that year? The English page of Wikipedia is not as clear as the Chinese page, which states that “中华人民共和国主席”职务自1954年召开第一届全国人大以后开始设立；1968年开始悬空；1975年通过的《宪法》删除有关“中华人民共和国主席”的条款，取消此一职务；1982年通过的《宪法》恢复了主席和副主席设置。 （The office of "President of the People's Republic of China" was established in 1954 when the first National People's Congress was held. It began to be vacant in 1968. The constitution passed in 1975 removed the clause with regard to "President of the People's Republic of China" and abolished this position. The constitution passed in 1982 re-established the positions of President and Vice-President.)
China in the early 1980's saw a hectic if not tumult transition, politically and economically. One element in these changes was conformity with the standards in the rest of the world. It's no surprise that the English word "chairman" for "主席", as the head of state, is replaced with the more common and less ambiguous "president".
Etymology doesn't play any role in the translation. "主席" literally means "the mat of the host" (or "the primary mat" since "主" has both meanings). "Chairman" is the man or person in the chair, while "president" originally means "sitting in the front" (Latin "Praeses"). Neither is significantly closer in meaning than the other to the Chinese word. But since both "主席" and "chairman" have a noun component in them, could that have been the reason why the 1950's and 1960's Chinese translators chose "chairman" instead of "president" as the English translation?
Having found the time the translation switched, we may conclude that there were two state chairmen in the history of the People's Republic of China, Chairman Mao Zedong and Chairman Liu Shaoqi, the latter in office from 1959 to 1968. After that, all we have are presidents, from President Li Xiannian (1983-1988) to the just elected President Xi Jinping (习近平).
Note that we're talking about head of state in this short article; the "Chairman of the Communist Party of China" and "Chairman of the Central Military Commission" remain to be "chairman". In connection to that, there's one minor special case to be dealt with. Mao Zedong intended to transfer his power to Hua Guofeng, a paramount yet weak leader of China after Mao's death in 1976 for a short time. Because of his insistence on Mao's principles and practices, there was a brief period when the phrase "英明领袖华主席" (wise leader Chairman Hua) became popular. Since he was not the head of state, the title "Chairman" is not equivalent to the latter-day "President", but only "Chairman of the Communist Party" and "Chairman of the Central Military Commission", two titles he did assume. It's possible, however, that the Chinese people back then would care less about this distinction, and unknowingly but incorrectly consider him as a successor to Mao in his full rights, including the state-of-head title of "Chairman", now called "President".