Screen is 1 server to 1 client.
In screen each client session is a fork of the screen server. In tmux there's one server and many client forks iirc.
They also compose: a boo session is just a PTY running a program, so you can run tmux inside one if you want.
Of course, it's impossible to know for sure what was LLM processed or not, but some of your posts (like this one) are getting classified that way.