Chinese-Korean historical relations were quite complex, with fluctuating regards for each other depending on the respective dynasties and political power. The majority of the time China was understood as the stronger power which Korea yielded to, however in reality Korea maintained its own level of respect and equal status. Furthermore, Korea was not advanced just under Joseon, its preceding states such as Goguryeo or Goryeo enjoyed certain bilaterally fair relations with Chinese powers.
For most of its existence, "China" as a power was unparalleled in Asia. China was center in the All-under-Heaven mentality, surrounded by the Four Barbarians on all sides. China alone kept the world in check, its majesty and eminence allowing it to impart its civilization and order onto the lesser peoples. The barbarians thus gave tribute in acknowledgment of China's supremacy. The case should be stated that, this was a narrative China emphasized for itself, numerous times it came under military pressure, conquest, or influence from its neighbors, oftentimes from the steppe tribes to the north. Regardless, their sinicization proved the superiority of the Chinese civilization, and thus continued the grandiose narrative.
Roughly speaking, Korea was understood as a barbarian realm, it was considered to be part is the Dongyi group of the Four Barbarians. However its exposure, proximity, and cooperation with China and Chinese culture allowed it to become "civilized" and raise itself up as a junior partner of sorts. China saw itself as "granting" culture and knowledge onto Korea, its willingness to accept China's authority allowed it to prosper under the Chinese sphere of influence, and thus become an extension of Chinese existence. By conforming to its inferior place as a tributary state, it could reap the benefits of connections to Chinese society.
While various Chinese states tried to impart the tributary narrative onto Korea, some saw greater success over others. Military expeditions into Korea saw limited success. Although Cao Wei scored decisive victories over Goguryeo in 225, Cao Wei collapsed to the Jin which allowed Goguryeo to regain lost holdings. The Tang were somewhat more successful. Although the Tang-Silla alliance toppled Goguryeo in 668, Tang and Silla soon broke into war themselves, with Silla maintaining the Korea state south of the Taedong River. Korea could not be fully conquered by the Chinese, and this fact was important in forging diplomatic relations between the two realms. China could not directly assert its ways onto Korea as it could within its own borders, and thus understood the limits an independent Korea held. However, its cultural and institutional significance constantly kept Korea close, and in effect kept the Korean court and government reliant on Chinese customs and dictates.
Let us take the case of Goryeo with Liao and Song for example. In the wake of the fall of the Tang Dynasty, no power filled its position in dominating East Asia until the Mongols. While the Song had some success in reunifying parts of the Chinese realm, soon the Liao Dynasty assumed control over northern China, with Southern Song surviving south of the Huai River. Both these states saw value in maintaining favor from Goryeo, who could shift the power dynamics. Suddenly Korea became a major player in East Asian political developments, and this allowed itself a position of autonomy, even if it officially functioned within a semi-tributary system.
In this time Goryeo strengthened itself domestically. For example, by promoting education and importing scholarly and Confucian books from Song China, publication became quite prolific, so much so that later on Chinese states imported and transcribed rare books only avaliable in Goryeo.
Goryeo in its relations with Liao, and later on, Jin, understood the importance of keeping these neighbors appeased, yet it increasingly found itself asserting its own independence without reliance on the Chinese authority. Indeed, this gave rise to Korean-centric ideas, with some officials stating Goryeo as the center of the world, and the existence of multiple "Sons of Heaven" with regard to the Goryeo King/Emperor as one of them. This is a striking notion as it reveals a pluralist worldview that both exposes the power of native Korean identity and an awareness that it is not alone with the Chinese to the west. The Goryeo ruler was Emperor at home and King abroad, it was pragmatic in diplomacy, keeping the Chinese appeased while modeling its own imperial and Confucian structure from China. Thus, in its feud and struggle between Liao and Song, neither could treat Goryeo as a tributary state and inflict dominance in the way Han or Tang could have. These Chinese states regarded Goryeo as an equal partner, and cordial diplomacy was necessary for their own interests in the heartland.
What we can understand from this is that in periods of disunity, China could not assert its military strength onto Korea and thus was unable to directly influence it. However, should China unify under a powerful state, such as the Tang Dynasty, Korea felt its weight and was forced to recognize the centralized power.
Joseon is undeniably the most sinicized Korean state. It heavily adopted Confucian values, which reinforced China-centric worldviews over the Korea-centric stance from the Goryeo. Joseon society heavily emphasized mastery of Confucian texts and its nobles were rigorously educated on Confucian values. The entire nation was governed under a rigid Confucian system, and this granted Joseon more favorable views from the Chinese, which saw this as the continued extension of civilizing and lifting up lower barbarian peoples. Joseon was "little brother" to the Ming, its Kings sought confirmation from the Ming Emperor when ascending the throne, and it participated in the tributary system fervently. Envoys were sent yearly from Joseon to give wishes and regards to the Ming court on the New Year, and both states dispatched envoys whenever Kings and Emperors ascended the throne and passed away. Joseon exports to the Ming were highly prized, its paper, writing brushes, and intricately decorated mats in particular. Joseon paper was very well regarded by the Chinese, its durability, smoothness, waterproof traits, and colored variations being valued for numerous applications. Technology and sciences were also well received by the Chinese, notably Joseon's developments and advancements in printmaking. Famously, Joseon was praised by the Ming as the “country of courteous people in the East."
The Ming Dynasty however can be characterized for their shift towards isolationist policy, moving China onto an inwards focused path that would continue into the Qing. As a result, the Ming granted Joseon a great deal of independence and autonomy, despite formal and ritual court dealings. Nevertheless, the Ming would come to the aid of Joseon during the Imjin Wars when the Japanese invaded. It should be stated that Chinese armies brought their share of havoc and destruction in their activities on the Korean peninsula, which indicates some degree of inharmonious regard between the two groups.
When the Ming decline in the 17th century, the Manchus twice invaded Korea and formally severed ties between Ming and Joseon. When the Qing Dynasty was formed, Korea retained its tributary status, as well as respecting its independence and territorial integrity. Although the Qing took up the mantle of Chinese civilization and center of the world, the Joseon themselves disdained the barbarian Manchus and maintained nostalgia and traditions from the Ming. Although increasing contact with Western powers shook up the Chinese-centric "All-under Heaven" worldview, the Qing kept an optimistic outlook on themselves as the central state and continued to recieve tributes. And though Joseon still recognized the authority of the Qing Emperor, it had effectively detached cultural attachment to the Qing Dynasty. This separation of identity eroded any favorable and amicable outlooks the Qing might have had on Korea, and with its weakening power in the ninteenth century, its policy on Korea became that of submission and compliance over "big brother-little brother" cooperation.
In conclusion, Korea was understood as a capable, civilized, and cultured society, however this was only assured because of its relationship to China, which bestowed many of the traits that made Korea respectable for the Chinese. Korea, as an entity separate to China, developed many praiseworthy qualities that earned the genuine appreciation and admiration from the Chinese, especially during the Joseon-Ming periods. Politically, Korea's existence was a series of contrasts, balancing its autonomous realm with a vassal tributary status.
Korea in relation to China is immensely complex and something I've sunken my teeth into only relatively recently. I've found more readings on the Korean view than Chinese, however I still find this useful in understanding the overall relationship. Historical narratives are marred by nationalist ones, and it's hard for me to keep a factual balance in these writings. It's late, I'm facing a power outage, and limited access to materials due to quarantine have kept me from providing as much as I would like, but I hope this helps. In the morning I'll polish this up and fix/add anything necessary.