My definition of K-pop has always been “Korean Idol pop heavily influenced by Western pop music and Japanese idol subculture targeting the youth population.”
I came up with this conclusion throughout my experience as a contributing writer of Idology (idology.kr), a K-poptimistic webzine which has been covering idols and idol-like musicians since the mid-2010s.
(I add the definition of idol as requested: an idol is a form of singer very popular in South Korea. The term originated from how Japan labeled young and pretty teenage singers from the 70s and 80s following the ye-ye girls from France in the 50s, like Matsuda Seiko. Most idols are trained from a young age, groomed to be good-looking and polite public figures as objects of love and role models to the youth population. As the idol industry has been around for more than 20 years, it no longer exclusively targets teenage fans, but is broadening its audience to a wide variety of ages and generations.)
Korean pop music has been around forever, but the terminology “K-pop” has been a thing since the early 2000s. TVXQ, one of the pioneers of K-pop success in the Japanese market, was labeled as either K-pop idol or “Hallyu (Korean Wave)” idol. Both terms were used in a mixed manner, but now “Hallyu” gives more of an outdated nuance. Maybe because it’s no longer just a wave? The prefix “K-” has been overused during the TVXQ-Kara-SNSD-Big Bang era, especially during the Lee administration. Because of the popularity of K-pop, the government may have thought it was a great label to put on anything to promote the country’s image, e.g., K-food, K-fashion, etc.
It is inevitable that Psy has been one of the best-known Korean pop artists, but in my humble opinion, he doesn’t quite fit into my definition of K-pop. He is actually quite rare in the style, and it’s hard to find his peers within the Korean music scene. His debut in 1999 stunned the nation in a bizarre way, as he claimed to be a comic (엽기, which was a trendy slang for anything related to cheap internet humor and B-film aesthetic at that time) dance singer. His target audience was a bit older than the usual targets of idols, perhaps from their 20s to 30s, whereas the usual target age is from preteen to 20s. I wouldn’t distinguish him to be a solid, ordinary example of K-pop. He’s not an idol in the first place.
To me, K-pop doesn’t include any particular genre other than one big category of Western pop music. I wouldn’t say K-hip-hop partakes in K-pop although there are many such artists collaborating with each other. If K-hip-hop and K-pop were equivalent, RM’s and Suga’s struggle during their early years would be a myth. There is a clear segregation between those two genres, based on the “authenticity vs. commercialism” argument, just like in any other country that has an established pop music scene. The only chance that the insiders and players of K-hip-hop gladly accept the label would be under one condition — if it sells better in the West.
K-pop is more of a music scene than a genre. A scene involves the idea of locationality. (I wouldn’t say nationality because the word gives a bit of an afterimage of nationalism…) EXO previously had four Chinese members; still, they were unapologetically K-pop. I find many idol groups from China or Thailand now have very similar look-and-feel with K-pop, and I agree with them being labeled as C-pop or T-pop, following the stylization of the term K-pop.