Angular is a client-side web framework that provides templating and data-binding. It was originally written in JavaScript, and now has a Dart port as well.
Somewhat relatedly, Google and Mozilla have been working on the web components standards, which bring some of the features Angular popularized, and some more fundamental ones as well, natively into the browser. These include Custom Elements, Shadow DOM, Mutation Observers, Object.observe(), and HTML Imports.
Polymer is a project that helps with building custom elements, it adds some sugar including templating and data-binding, similar to Angular in some ways, but completely focused on modern Web Components related standards, and on elements - not apps or frameworks. You can use Polymer elements in any app with any framework, or without a framework.
Web Starter Kit looks like a bundle tools to help you build a site with modern best practices, like responsive layouts, a local dev server, a build system, mobile-friendly user input, multi-device testing, etc.
Web Starter Kit looks like it's framework agnostic, so you could probably use Angular or other frameworks to fill in the views, though these days you might find you don't really need a framework if you're using Web Components.
tldr; it's more than compiling to JS.