What is the difference between ES6 and NodeJS?

Babel is a transpilation library. It takes ES6/7/Next code and compiles it down to a previous standard. It allows you to use ES6, some of ES7 and with plugins, things that are not officially part of the language yet. Babel is usually used to transform ES6+ code so that it can be run in a browser, many of which that are still in wide use only support ES5.

Node is a server-side javascript runtime, while you can use node to run babel'd code (it's just javascript!), you don't need to as node can understand ES6 on its own.