Both Korea and Japan are often regarded by historians as secondary states. A secondary state is one that came into being relatively late and was influenced substantially by an older civilization. These categories are not without flaws, because no civilization is completely pristine and original, but they do offer a way of making sense of relationships like those of China with Korea and Japan. A brief description of the early states in Korea and Japan will allow you to draw some comparisons and tease out some insights.
Han China is credited with founding the Lelang Commandery on the Korean peninsula around 108 BCE. Historians regard Lelang as having been a Han province. By this time, Chinese states had long been in existence, at least from the time of the Xia Dynasty (before 2,000 BCE) and on through the Shang, the Eastern and Western Zhou, and finally the Qin and the Han (226 BCE to 220 CE).
The Lelang Commandery disappeared around 313 CE, and then native kingdoms emerged, namely Koguryo in the north and Silla and Paekche in the south. These three kingdoms then competed for supremacy from about 300 to 668 and continued to be influenced by China, adopting both the Buddhist religion and the Chinese system of writing.
Most of what we know about these early states comes from archaeological evidence in the form of tombs and their contents, like ornaments and pottery. After the introduction of Buddhism in Korea, cremation eventually became the norm, meaning there are no tombs to examine.
Japan had diplomatic ties with China, also starting during the Han period. That said, Chinese influence on the early Japanese state came through southern Korea. The kingdom of Yamato, from between 250 and 300 CE, is the earliest known Japanese state. The primary source of evidence about the kingdom consists, like in Korea, of burial mounds. The most remarkable of these is the Nintoku "keyhole" tomb, surrounded by three moats. As in Korea, the adoption of Buddhism eventually led to the disappearance of tombs in the archaeological record. The extent of Korean influence on Yamato is an issue of dispute among historians. It is fairly safe to say that iron armor and weapons, as well as horse riding, came from Korea. That said, influence went in both directions, and the degree to which these states were organized and culturally distinct is still a matter of debate owing to the relatively scant evidence. In any case, the reality of exchange or borrowing suggests that the two cannot be studied in isolation. In the 500s and 600s CE, Japan came under more direct influence from China, when Japanese rulers adapted the Chinese script for Japanese writing, and political reorganization appears to have mimicked the Chinese model.
A quick online review of the artifacts found in Korean and Japanese tombs can provide valuable observations on their similarities and differences.