Words related to extinguish
Old English stician "to pierce, stab, transfix, goad," also "to remain embedded, stay fixed, be fastened," from Proto-Germanic *stik- "pierce, prick, be sharp" (source also of Old Saxon stekan, Old Frisian steka, Dutch stecken, Old High German stehhan, German stechen "to stab, prick"), from PIE *steig- "to stick; pointed" (source also of Latin instigare "to goad," instinguere "to incite, impel;" Greek stizein "to prick, puncture," stigma "mark made by a pointed instrument;" Old Persian tigra- "sharp, pointed;" Avestan tighri- "arrow;" Lithuanian stingu, stigti "to remain in place;" Russian stegati "to quilt").
Figurative sense of "to remain permanently in mind" is attested from c. 1300. Transitive sense of "to fasten (something) in place" is attested from late 13c. To stick out "project" is recorded from 1560s. Slang stick around "remain" is from 1912; stick it as a rude item of advice is first recorded 1922. Related: Stuck; sticking. Sticking point, beyond which one refuses to go, is from 1956; sticking-place, where any thing put will stay is from 1570s. Modern use generally is an echo of Shakespeare.
1560s, "recognize as different or distinct from what is contiguous or similar; perceive, make out," from French distinguiss-, stem of distinguer, or directly from Latin distinguere "to separate between, keep separate, mark off, distinguish," perhaps literally "separate by pricking," from assimilated form of dis- "apart" (see dis-) + -stinguere "to prick" (compare extinguish and Latin instinguere "to incite, impel").
Watkins says "semantic transmission obscure;" the sense might be from "pricking out" as the old way to make punctuation in parchment or some literal image, but de Vaan derives the second element from a different PIE root meaning "to push, thrust":
The meanings of ex- and restinguere 'to extinguish' and distinguere seem quite distinct, but can be understood if the root meant 'to press' or 'push': ex-stinguere 'to put a fire out', re-stinguere 'to push back, suppress', and dis-stinguere 'to push apart [thence] distinguish, mark off ....
The suffix -ish is due to the influence of many verbs in which it is the equivalent of Old French -iss-, ultimately from Latin inchoative suffix -iscere (this is also the case in extinguish, admonish, and astonish).
Sense of "to mark or note in a way to indicate difference" is from 1570s; that of "separate from others by some mark of honor or preferment" is from c. 1600. Intransitive meaning "make a distinction, find or show difference (between)" is from 1610s. Related: Distinguishing. The Middle English form of the verb was distinguen (mid-14c.).
early 15c., "annihilation," from Latin extinctionem/exstinctionem (nominative extinctio/exstinctio) "extinction, annihilation," noun of action from past-participle stem of extinguere/exstinguere "quench, wipe out" (see extinguish). Originally of fires, lights; figurative use, the wiping out of a material thing (a debt, a person, a family, etc.) from early 17c.; of species by 1784.