Close is one of those annoying words with a million definitions and a pronunciation that changes depending on the context. Honestly, I’m just glad that all the different forms are related because I’ve had it up to here with words that randomly sound alike but are completely different. Anyway. Enough rambling. Close as in shut showed up in the thirteenth century, which was a century before close as in near. Both words come from the Old French clos-, the past participle stem of the verb clore, to shut (it took on the connotation of “closing a gap”, hence near). That word is from the classical Latin clausus, closed, from the verb claudere, to close. That can be traced all the way back to the Proto Indo European klau- which means… hook? What?
Finish first showed up in the late fourteenth century, from the Old French finiss- the past participle stem (two in a row here) of fenir, to finish. It’s from the classical Latin finire, to limit or end, related to finis, end or boundary. It might be related to figere, the origin word for fix, but it’s definitely related to finite.
Final is of course also related, just with a slightly different origin. It showed up before finish, in the earlyfourteenth century, from the Old French final and Late Latin finalis, concluding or final. And that of course is from finis. Yeah, this one shouldn’t be a surprise to anyone.
Cease showed up in the fourteenth century as cesen, to stop moving/acting. It’s from the Old French cesser, with basically the same meaning, and classical Latin cessare, which is just to stop. That’s from another Proto Indo European word, ked-, which is the origin for pretty much anything with -cess or -cede in it.
Terminate showed up in the early fifteenth century from the classical Latin terminatus, terminating. That’s from the verb terminare, which is just to terminate. That one’s obviously related to terminal, which showed up in the mid fifteenth century from the Latin terminalis, the adjective form of terminare.
No great mysteries here. I’m kind of relieved. This one was pretty straight-forward.