Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.
word-forming element used in forming nouns from Latin words ending in -atus, -atum (such as estate, primate, senate). Those that came to English via French often arrived with -at, but an -e was added after c. 1400 to indicate the long vowel. The suffix also can mark adjectives formed from Latin past participles in -atus, -ata (such as desolate, moderate, separate); again, they often were adopted in Middle English as -at, with an -e appended after c. 1400.
Latin adjectives in -orius, according to "An Etymological Dictionary of the French Language," tended to "indicate a quality proper to the action accomplished by the agent; as oratorius from orator; laudatorius from laudator. The neuter of these adjectives was early employed as a substantive, and usually denoted the place of residence of the agent or the instrument that he uses; as praetorium from praetor; dormitorium from dormitor; auditorium, dolatorium.
"These newer words, already frequent under the Empire, became exceedingly numerous at a later time, especially in ecclesiastical and scholastic Latin; as purgatorium, refectorium, laboratorium, observatorium, &c." [transl. G.W. Kitchin, Oxford, 1878]