Yep, that's a context thing though. In some cases, greek people replace "a moment" with "a minute". "Wait a moment/minute - Περίμενε μια στιγμή."
"I'll be down in a moment/minute - Θα είμαι κάτω σε ένα λεπτό"
"One moment, please - Ένα λεπτό, παρακαλώ" In other words, sometimes "λεπτό" και "στιγμή" have the same meaning. ^.^
I have to say I disagree, in every phrase you give as an example it is clearly moment = στιγμή and minute = λεπτό. The fact that using either is correct does not mean that their meaning is the same. Only the context in your examples is the same, and that gives a general same-y not literal meaning, but the words are not to be used interchangeably.
There is one particular turn of phrase where usage is usually different between the two languages: in English, people mostly say "the last minute" but Greeks leave things to be done at "the last moment". There are obviously many moments to spare within a minute! :)
Of course the context is never exactly the same, since we are talking about two different words, with different meanings, used for different phrases, But as a native greek speaker, at least in spoken greek, I've noticed that it really doesn't matter to people. They might use the word "minute" instead of "moment", and no one will ever notice a difference.
And yes, there are some cases that you can't really replace "moment" with "minute", especially in english. I guess I shouldn't have said "..have the same meaning", but I meant that either of those is okay in that example, and other cases like the one of "waiting". Always talking about greek. But I can see your point, I agree about the difference in meaning. ^.^
This noun, η στιγμή, is the same in ancient Gk and means a very short duration of time, i.e., moment. Perhaps less helpful is ancient Gk λεπτ- stem which often conveyed smallness or fineness: adjective λεπτός, ή, όν small, fine; delicate, etc. and was used in compound words e.g., λεπτόγραμμος, ον written small or neat (LSJM 1039). My point is that it can be helpful if a person comes to modern Gk from ancient with a word such as στιγμή, whereas it seems to me that modern Gk helps someone trying to do ancient Gk with a word such as λεπτό because it rarely is attested in ancient Gk in the sense "minute" except in specialized astronomical literature (LJSM, 1040a). And yet at least as early as the Byzantine period λεπτός is attested with the sense "minute" (Lampe, Patristic Gk Lexicon, 798), and it's probably found in that sense in the papyri, which probably hints at the gradual diachronic association of the lexeme in the sense "minute." Thank you to our moderators for discussing λεπτό and στιγμή.
Well, the minute couldn't have a translation in ancient Greek, because when ancient Greek was spoken there was no minute (or second). With the exception of astronomy, clocks were not used or needed in ancient times. And they used sundials and waterclocks. The minute is much younger and was "invented" in Arab world and then exported into Europe around 1000 years ago.
Thank you. Your comment is really helpful. Have a lingot. I found this explanation online that discusses the Egyptians and traces the minute back to Claudius Ptolemy ca. 150 CE. However, the article doesn't discuss in depth when people actually used "minute," so maybe that was through Arab influence. https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ The article just says that in the west it became common in the 16th century through mechanical clocks. Also, mizinano has an interesting comment here: https://forum.duolingo.com/comment/18358553