Streamlit uses a responsive way to get input and doesn't rely on callbacks at all. Every time a user interacts with a widget, your script is re-executed and the output value of that widget is set to the new value during that run. It's amazing but also a little hard to understand.
In contrast, the way of writing PyWebIO app is more like writing a terminal program, except that the terminal here becomes a browser. The output functions will output content to user in real time, and the input functions will block until the user submit the input form.