Is Babel used to produce backward or forward compatible Javascript code?

I have been reading through a book called You don't know JS and one thing that I can't wrap my head around is the concept of backward compatible and forward compatible Javascript.

From what I understand:

1. Backward Compatible: Once something is added to Javascript specification, it would never become invalid JS in future
2. Forward Compatible: Including a new addition to the language in a program would not cause that program to break if it were run in an older JS engine

Javascript is backward compatible and not forward compatible. This means that while including new feature in a program might break the program (forward compatible), Javascript engines would support older syntax forever in future (backward compatible).

To solve a problem of forward compatible issue, developers use transpilation and polyfills to convert new syntax to an older syntax supported in older Javascript engine.

So if transpilation is used to convert code into forward compatible code, does that mean Babel is used to solve forward compatibility issue and not backward compatibility issue?

This comes from the official doc in Babel website:

Babel is a toolchain that is mainly used to convert ECMAScript 2015+ code into a backwards compatible version of JavaScript in current and older browsers or environments.

I must have missed something and need some clarification on how to think through this.

Edit 1

I thought it would be helpful to quote parts of the book here:

Typically, forwards-compatibility problems related to syntax are solved by using a transpiler (the most common one being Babel (https://babeljs.io)) to convert from that newer JS syntax version to an equivalent older syntax.

Developers should focus on writing the clean, new syntax forms, and let the tools take care of producing a forwards-compatible version of that code that is suitable to deploy and run on the oldest-supported JS engine environments.

I believe your confusion is rooted in the mixing of the forwards- and backwards-compatibility terms for both the operating environment or language, and individual scripts themselves.

In the You Don't Know JS doc, the writer is describing the implementation of the language as whole as being backwards compatible, in the same way that many video games released for early generations of consoles (such as PlayStation and XBox) are able to played on their more recent successors (PlayStation 2 and XBox 360) due to the console (and its architecture, operating system, etc) being backwards compatible. When applied to JS, this means that a browser implementing a newer version such as ECMAScript 2015+ will fully support code written using an older version.

Babel, on the other hand, is referring to the code itself, and being able to create a backwards compatible version which can be run on older browsers, for example. To expand on the example above, this would be akin to being able to process an XBox 360 game through some engine (i.e. Babel) and have it give you a fully functional game to play on your original XBox. This is clearly a much more difficult problem, but is required due to JS not being forward-compatible.