The essence of what you said is correct.
The underlying reasons though are not quite clear. In US, the underlying socioeconomic political system is "adversarial", as in everything is about you against someone else. You compete for resources, jobs, etc.. So, speech in US is viewed also in that "adversarial" light. It's allowed to be "adversarial", competing in the "market place of ideas", with limits (1. don't incite violence, 2. don't cause so much hostility to provoke others to violence, 3. national security, etc.)
In theory, China's censorship works with similar standards. But China's overall socioeconomic political system emphasizes on "non-adversarial" or cooperation approach. So, if someone's speech is viewed as mainly designed to provoke adversarial reactions from others, as would be reasonably understood by objective 3rd parties, then such speech are generally not allowed. (Because the benefit of such speech are so minimal and the harm of adversarial confrontation could be so high).