socket.io - middleware vs running after connection

Question

I'm working with socket.io for the first time to setup auth.

Whats the difference between using a middleware vs running a function after connection?

Ref: https://socket.io/docs/v4/middlewares/

// middleware
io.use((s, next) => {
 if (isAuthed(s.request)) {
  next();
 } else {
  next(new Error("invalid"));
 }
});

vs

// after connection
io.of("/").on("connection", (s) => {
 if (!isAuthed(s.request)) throw new Error("invalid");
 ...
});