Babel’s stage presets equate to the TC39 Process and the different states of each proposal for a potential language change. They include implementations and polyfills for all of the proposed changes in that stage.
Anything currently in Stage-0 is Strawman, not ES6. It is future Javascript and absolutely not certain that it will ever make it into any official ECMAScript specification.
Please do not just set to stage-0 so it will work without understanding the consequences this will have.
The Babel Preset which contains only ES6 features is preset-es2015