Communication with ESP, HTTP requests or WebSocket?
This way it looks more professional but Is it more efficient?


No, the differences are minuscule. It's only really the location of any parameters that are different - either as part of the URL (GET) or as part of the body (POST).


  Is this using websockets? Is using websocket a better way? is it more robust?


No, it's just a TCP connection (or maybe UDP connection, it's hard to tell from your description) sending unknown data. It's impossible to tell what the data us from the port number, you would have to actively sniff the data and work out what it is.

Yes, it is generally more efficient doing that kind of thing (though not necessarily more "robust") - HTTP is a very generic system that can transfer many different kinds of data in a request so needs large amounts of superfluous information that is not applicable to controlling an LED, whereas a simple TCP or UDP socket only transfers the minimal amount of data needed to get the job done.