Most censorship in China is done by the private sector. It doesn't come direct from the government. Instead, the government makes it clear that various types of speech are deemed unacceptable, but remains vague about exactly what. For example the PRC likes to crack down on "rumours".

The consequence is that the private sector is a huge and critical part of how China censors information. Actual direct government censorship is relatively limited: it's all based on distributing vague principles to the private sector combined, with punishments for failure to comply. The result is people interpreting the principles in the most aggressive way possible.

In the west, governments have egged on progressive agendas and passed laws that punish various kinds of speech (e.g. "hate speech"). But most of the censorship is done by the private sector, who are trying to interpret vague principles in ways that'll avoid them being targeted for punishment. The fact that in the west the media and various ideological groupings have as much to do with it as a government agenda doesn't change the fact that most of the ensuring censorship is still run and managed by the private sector.