China is a rising power in the world and wants to at least be the primary power in its region (maybe the world, who knows), and the USA as the primary power in the world and the region wants to keep its position. The US and China also have a symbiotic relationship, China would not be able to be in the position it is today if not for American purchases, and Americans would not have the quality of life they currently enjoy if they did not have Chinese manufacturing.
Both countries know they cannot be openly hostile to each-other without huge ramifications so they use proxy conflicts to try to secretly bludgeon each other and propagandize their own populations. Americans can propagandize their population with HK, Taiwan, concentration camps, no freedom and Chinese can propagandize their population with drone strikes, Century of humiliation, US Imperialism... Nobody, except the misled population (who are being propagandized) or extremely dim-witted subsets of elites (who are doing the propaganda, and go high of their own supply so to say) actually care about these issues.
I do not think this will be as hot as the last cold war since the US and China are way more interdependent than the US and the USSR and the way to make sure that this semi-cold war will not turn into a hot war is to not trying to break the interdependence, but to strengthen it.