> How are LLMs not statistical models that predict tokens?

there's LLMs as in "the blob of coefficients and graph operations that runs on a gpu whenever there's an inference" which is absolutely "a statistical model that predict tokens" and LLMs as in "the online apps that iterates and have access to an entire automated linux environment that can run $LANGUAGE scripts and do web queries when an intermediary statistical output contains too much maybes and use the result to drive further inference.".