China's is possessive. It shows that China owns something or that something belongs to China. Chinese is an adjective, describing the target noun as being a part of China or specifically refering to a Chinese variant of it. I don't think it is a matter of formality rather than distinguishing between the nation and the people and proper grammar. For instance, in news they may say "China's decision to..." rather than "The Chinese decision to.." because the decision itself isn't Chinese. You could reword it as "The decision of the Chinese to.." but it can upset the flow of the sentence, and really in a case like this you want to refer to China as a nation rather than a people, so "China's decision.." would be more appropriate.