The actual implementations are licensed depending on the implementer. Adobe, Apple, Google, Microsoft, the Mozilla Foundation, and Opera Software are the most prominent of these.
Each will have their own licensing, Mozilla for instance uses MIT.
If you wanted to do your own implementation for your own from scratch web browser, then you'd have control of the licensing as they would be your implementations of the standard.
Otherwise, I'd go with whatever license the base implementation you're using uses. That is, whatever layout engine and JS VM you're building on. For instance, node.js is built on top of Google's V8 engine.
The copyright license of the language specification. This license covers the actual text that describes the definition of the language. The licenses can vary between languages, but they typically do not allow modification of the text and sometimes do not even allow copying (especially if the organization that publishes the specification tries to make money from selling copies).
The two licenses under 1 and 2 are not related to each other in any way and for any specification you can have multiple implementations using a variety of licenses.
In a sense, the language itself is considered to be no more than an idea, which can't be copyrighted. The specification and implementations are different expressions of that idea and are independent as far as copyright is concerned.