I dont think tiktok app is banned because of algorithm, because bytedance created and maintains both Doyin and Tiktok.
I think it is form of compartmentalizing Internet and social networks, to keep Chinese internet and social media separate from the US.
the red book app, where tiktok refugees are flocking to right now, also want to introduce geofence and compartmentalize Chinese users and US users separately
Tiktok is banned completely in China because it doesn't not have the agressive filtering and CPP propaganda in place to operate in China. The CPP can not allow Chineze citizens to engage in an open exchange of ideas with eachother or with the citizens of other free nations, for obvious reasons.
You are making a distinction without a difference. China knows TikTok is harmful, which is why it allows it's export and bans domestic consumption. Think of it like a drug.
It’s not just about controlling content but also about controlling how users interact across borders