Difference between Events and Functions?

Events deal with asynchronous operations. They aren't really related to functions in the sense that they are interchangeable.

eventEmitter.on is itself a function, it takes two arguments the event name, then a function (callback) to be executed when the event happens.

eventEmitter.on(evt, callback)

There is no way to tell WHEN the event will be emitted, so you provide a callback to be executed when the event occurs.

In your examples, you are controlling when the events are triggered, which is different than real world use where you may have a server listening for connections that could connect at anytime.

server.listen('9000', function(){
    console.log('Server started');
});

server.on('connection', function(client){
    console.log('New client connected');
    doSomethingWithClient(client);
});

//series of synchronous events
function doSomethingWithClient(client){
    //something with client
}

For server.listen the server doesn't start immediately, once its ready the callback is called

server.on('connection') listens for client connections, they can come at any time. The event is then triggered when a connection occurs, causing the callback to be run.

Then there is doSomethingWithClient this is just a function with a set of synchronous operations to be done when a client connection occurs.