There is an incredible amount of diversity between the regions you have listed above, and it would be impossible to list out every difference here. But keep in mind that "Asia" is a catch-all term, and implies a level of homogeneity that doesn't actually exist between any one of these countries. In the first place, Vietnam and Thailand are actually considered to be a part of Southeast Asia, while China, South Korea, and Japan are a part of East Asia. And beyond this very superficial geographic distinction, these are all vastly different places.
Linguistically, China and Japan share a similar script. In fact, the Japanese gradually adopted Chinese characters for several of the early centuries of its development (with particular intensity around 794–1185) because it lacked a written script of its own. However, Chinese, Japanese, and Korean are all derived from different language families, and it is therefore very difficult to trace all of them back to a common ancestor language. The Thai language is one member of the Kra-Dai language family, which predominates in central Southeast Asia and parts of northern India. Thus, some dialects in countries like Laos, Cambodia, Myanmar, and in certain Chinese provinces are closely related to the Thai language. Vietnamese, like Korean, is a part of an isolated language family (though this fact is debated by linguists), and therefore cannot be subsumed into the larger, Thai-speaking parts of Southeast Asia.
When considering the cultural influences of this region as a whole, it is difficult to ignore the central position of China. Throughout much of its ancient and medieval history, China was a major imperial power in both Southeast Asia and in the East China Sea (which touches both South Korea and Japan) and therefore spread its culture widely across this vast territory. In the case of Japan, we saw how this impacted the development of writing. But major philosophies, such as Buddhism and Taoism, also reached Japan by means of Chinese interaction. Furthermore, China exported its unique system of examining individuals for public office, known as the "civil service exam" across the Asian world, and many different regions, from Japan to Vietnam, adopted it as a way to select individuals to hold high office. Finally, Confucianism, so central to Chinese understandings of ethics and morality, permeated the discourses of other regions as well, particularly the kingdoms that came to power in northern Vietnam.