'Common Prosperity' seems to mean that there are too many rich people in China that are giving too little money to the central government as their wealth usurps the power of the CCP.
"Tax the rich" in the US is just a slogan. In 20+ years I've been in the US I've yet to see it actually yield anything concrete. Taxes on the middle class have grown substantially in the meanwhile (health insurance is 3x what it was 20 years ago, and it is a tax in all but name, real estate taxes are 4-5x, and you now pay local sales taxes on interstate online purchases, too).
I mean the NYTimes[0] gave a glowing interview to the creator/designer of AOC's 'Tax The Rich' on September 21 but never once mentioned that the designer owes a considerable amount in taxes in multiple states[1] which had been published 3 days prior by another newspaper.
It's more nuanced than that. In America calls for raising taxes are usually in the name of some public good, eg infrastructure. How true that is is up to personal interpretation. In China it's purely about power, namely removing any semblance of power held by non government entities.
Well, no, in China it's in the name of socialism - of the prosperity and well-being of the less well off. How true that is is not really up for personal interpretation - it's just false. (Of course, one could argue the same about the US...)