ECMAScript is the basis of Javascript. Is a lot of specifications, that determine what the Javascript has. The majority browsers supports ECMAScript 5.
Recently, the Ecma define a new version, called EcmaScript 6, or just ES6. So knowed by Ecma 2016, because the target now is release new things anually.
To use ES6, ES7, you dont need a browser/Node.js with support to their. You can use libraries to transpile your code up-to-date in ES6/7, ..., to ES5, and have full support. An example of an excelente library to tranpile Javascript is the Babel.
Babel allow you to use new things of Javascript today :D.
Has many ways to tranpile using Babel in different environments. Look here
If you use Node.js, I suggest you to update to an version greater or equal to 4.x, because that have support to many things in ES6.
In our articles, I suggest you to use Node.js to run your javascript, is the way most fast.
But, if you are in the browser, you can use tools like Gulp, Webpack, Grunt, and is really easy found tutorials in web about theses.