I think China and Russia want the exact same thing: a return to historical glory for their respective nation. Russia wants to be the big 800lb gorilla that they were as the USSR striking fear into the hearts of people with the looming threat of the Cold War. China looks back on their history as a huge dynasty that was beset by the west in the form of direct intervention or indirect (i.e. drugs). Everyone has been willing to let China abuse its populace to serve as a manufacturing hub for the garbage that we just throw away in a year (tops), and they've now got good amounts of capital and production capability to use as collateral to avoid western mingling.
I don't know about Russia, but as someone of Chinese descent, I can say for certain that the Chinese are still indignant about how almost every major foreign power has abused it while it was weak. This is a major driving force for China. They never want to be in a position where they are humiliated again. For all the thought about how sleazy Chinese are in business dealings with the west, remember that it is because of their "win at all cost" attitude where they never want to be under the heels of a foreign power again. Just look up China's Century of Humiliation if you're interested in the thought process behind China's government. China remembers, even if you don't.
With that said, while the average Chinese still remembers, most Chinese just want to live a normal life. As much as there are horror stories about the oppression of the Chinese government against its citizens, the average citizen lives a relatively normal life. And they just want to be able to enjoy life as a child, grow up, fall in love, marry, and have children. Same as anyone else in the United States. I know for a fact our suppliers (both in China and Europe) are unhappy with the Russian invasion of Ukraine as it has played havoc with exchange rates and is affecting their livelihood.
Side tangent.
This was from another thread where I said I felt China had some valid claims to Taiwan, and that if push came to shove and China invaded Taiwan, I thought the US would only provide limited support. Similar to what the US is giving to Ukraine now. Some thought i was pro-China and hoping for a Chinese invasion of Taiwan. That is actually false. I would love for the US to actually officially recognize Taiwan as a sovereign state and pledge to defend it. At this point in time, I think the world is a better place if Taiwan remains free, and not under the rule of China.
The reason I bring this up is China is watching the Russian invasion of Ukraine very very closely. The US needs to provide a stronger response. Or else China will be emboldened into taking action, sooner rather than later.