This question basically makes it sound like the node library Socket.io uses the library engine.io which uses ws.
What role do each of these play given that each one can independantly create a WebSocket connection?
Look at Introducing Socket.IO 1.0 - New engine to see why they made Engine.IO.
Engine.IO has all the browser hacks and different things for compatibility, and has modularised the Socket.IO codebase.
You are correct that Socket.IO uses Enginge.IO which uses ws.
Socket.IO handles: