In English, there is a pretty well understood division between "white meat" and "red meat". Likewise, people will talk about "light/dark meat" when eating certain meats.
What sorts of meaningful distinctions between meats are commonly made in Korean? Are concepts like "red meat" well understood?
I looked up 붉은 고기 "red meat" a bit, but my impression is that this is a relatively recently borrowed term.
Interesting inquiry.
Generally, in Korea, there does not exist a differentiation between meat based solely on its appearance i.e. color an or texture. Rather, each separate sections of meat can be identified specifically by name. Nonetheless, there still exists terms such as 붉은 살코기, 흰 살코기 which in fact are primarily used in both heath and medical fields.
As for dark chicken meat, know by 순살 or "순" they loosely translate to their English equivalent. Pure, weak, soft or just plainly white meat. And as for the chicken breast, it's Korean translation would be 닭 가슴살. I hope this gives you a better understanding.
As you've mentioned in your question, there were no such words which correspond perfectly to the english words. But now there are new terms. According to HiDoc, a news media for medical doctors, 흰 고기(=white meat) and 붉은 고기(= dark meat) are officially used.
http://www.hidoc.co.kr/news/healthtoday/item/C0000002377
The title of the article means "To prevent breast cancer, rather eat white meat, not dark meat".
