ECMA is an association for standardizing information and communication systems. ECMA standardizes JavaScript under the name of ECMAScript.
In a nutshell ECMAScript is a standard while JavaScript is the implementation of this standard.
All name like ES1, ES2, ES3, ES4, ES5, ES6, ES7, etc., are abbreviations of the ECMAScript version.
ES6 was issued in 2015 and also called ES2015. As of 2015, all new versions of ES are supposed to be named by the year - ES2016 (ES7), ES2018 (ES8), etc.
ES.next is the abbreviation of all upcoming, not standardized yet versions.
The ECMA standard is supported by browsers. The following table provide extensive information about the browser support, feature by feature:
https://kangax.github.io/compat-table/es6/
In order to provide better browser support, tools like Babel can help you use latest JavaScript features into older browsers. Babel is a JavaScript compiler, more precisely said - a transpiler, that allows developers to program using ES6 feature converted to a Javascript code that current browsers can process. React (ReactJS) is a great example of Babel usage.
