As a history graduate, I know it has been a common sense in history that 高句(gou)麗 is quite different from 高麗. 高句麗 or 高句驪 was the nation founded by one of the nomadic people originated from now northeastern part of China and later entered into northern Korea peninsula around 4th-5th century, whereas there were already two agricultural nations in the southern part of the peninsula, which were believed that the people there had been descendants of ancient Chineses from Shang(商).
During mid 7th century Dynasty of Tang annihilated 高句麗 and set its newly-acquired domain with four administrative units. Tang also removed all royal families and wealthy people of 高句麗 to the inner part of China. After Tang perished, the peninsula was unified under the name of 高麗 during the era of "Five Dynasties and Ten Nations" in early 11th century. Henceforth the regimes in the peninsula had become a vassal state to unified China empires until 1895.
An erstwhile classmate from South Korea( a Korean, not an expatriate Chinese) argued with other classmates that Chinese women are prettier than Korean women, and he insisted on his "viewpoint" because he deemed China seized all pretty women from Korea during Tang Dysnasty and left the ugly ones in the peninsula. We then reminded him of the fact stated above, but in exasperation he claimed 高句麗 was part of Korea. Well, we didn't want to argue with him any more, but what he claimed reflected the mindset of Korean people that northeastern part of China's territory, or even larger, is their "intrinsic land". I haven't heard of that Korean classmate since I grauated. Probably he became a teacher in Korea and continued to teach his students the "Histroy of Korea" in that way.
Attached below please find a more detailed account about such a "common sense". https://www.toutiao.com/a6484105357114212877/