Earlier quoted context omitted.
The term could refer to either South Korea or Korea as a whole, depending on the context. As for your example, I think people would agree with (b) because when you're talking about populations people implicitly assume we're talking about a country. On the other hand, people say "Korea's history reaches back thousands of years," and obviously here "Korea" means Korea as a whole (the country of South Korea wasn't found…
Thanks for the explanation! > I think people would agree with (b) because when you're talking about populations people implicitly assume we're talking about a country. Yeah, that makes sense, but the confusing part for me is that, at least if my understanding is correct, the South Korean government doesn’t legally recognize the partition of Korea. So they think all those 80 million people are rightfully citizens of t…
But everyone understands that this is a legal fiction. Despite mutual hostility, the two Koreas are somewhat relaxed about interpretation: for example SK doesn't object to other nations establishing diplomatic relations with NK, and vice versa.
Depending on who you ask, you'll hear different views on how to reconcile the law with reality, ranging from "there is only one rightful government, and a group of commie rebels we should destroy" to "we should accept that there are two different nations" to "South Korea is but a colony of American Imperialists!" But anyway, everyone accepts that practically there are two countries, so when we're talking about any contemporary matters, we're usually just talking about South Korea. (Unless we're specifically interested in North Korea.)