Four dictionaries I consulted gave presidentship as a synonym of and definition for presidency. Both appear to mean the office, tenure or term of a president.
Presidentship is a regular formation for a noun with this meaning, adding -ship to the title of office.
However, I have never encountered the word presidentship; and upon Googling the word and tracking hits through ten pages I found it used only in a) dictionaries, b) a few personal posts by persons who are evidently not native speakers and c) a fairly large number of pages about Indian politics.
I conclude from this that there is no difference in meaning between presidentship and presidency, but presidentship is the preferred term in Indian English, presidency in other English speech communities.
EDIT:
@Kris suggests that “presidentship comes in very handy where you need to refer to that state while distinguishing from the office,” and cites Wikipedia s.v. Edward Martin(Queens’ ). That distinction would indeed come in handy; but the passage in question does not draw it. The facts to which it alludes are that Martin was arrested and removed from the state of exercising his office on August 30, 1642, but was not removed from the office — as Wikipedia puts it, “ejected from the presidentship of Queens’ College” — until March 13, 1644. (Grey, The Queens’ College (1899), pp. 163, 171).
Presidency and presidentship have historically been in free variation. Indeed, Mullinger, University of Cambridge from the Earliest Times ... (1873) uses both on the same page (446), with no evident distinction: “[Fisher's] election to the presidency of Queens’ College”, “when [Fisher] resigned the presidency”, and, in a footnote, “[Wilkinson] succeeded Andrew Doket in the presidentship in 1484”. So also Thomas Thomson, History of the Royal Society (1812) page 12: “the presidency of Martin Folkes, Esq.”, “the presidentship of the Earl of Morton”, “the presidentship of Sir John Pringle”. Modern writers appear to have achieved greater consistency by restricting themselves to one term or the other.
From Chambers Dictionary:
“-ite” is a suffix used to “form names of people, indicating their origin, place of origin, affiliations, loyalties” (e.g. Jacobite). Whereas suffixes “-an” or “–ian” denotes “things belong to or typical of a specific person” (e.g. Johnsonian).
I couldn't find anything on -ist. They generally all mean the same thing though and I assume the reason we have all three in English is so there is always a good aesthetic/phonetic fit for various situations.
Best Answer
From Wiktionary :
-istAnd :
-erThe etymology part says that :
-istcomes from Latin-istafrom Ancient Greek -ιστής (-istḗs), from -ισ (-is) + agent suffix -τής (-tḗs)...-ercomes from Middle English -er, -ere, from Old English -ere (agent suffix), from Proto-Germanic *-ārijaz (agent suffix). Usually thought to have been borrowed from Latin-āriusfrom Proto-Indo-European relational adjectival suffix *yo- (“belonging to”)...Used to form adjectives from nouns or numerals.
(masculine only) -er; Used to form nouns denoting an agent of use, such as a dealer or artisan, from other nouns.