I read both of the links below
http://en.wikipedia.org/wiki/ECMAScript
http://stackoverflow.com/questions/912479/what-is-the-difference-between-javascript-and-ecmascript
My question is, does ECMAScript exist as something I can download and use instead of JavaScript?
It's just a standard to dictate the implementation of a "javascript" language, it's not something you "download and run". You can write your code against the ECMAScript spec and pretty much expect it to run on all the "javascript" interpreters (or that's the idea anyway ;-))
As far as I know there isn't a validation suite for testing your code against ECMAScript, but it's not something I've ever felt a need for.
ECMAScript is a language.
What we have in browsers (and other clients) is ECMAScript-compliant implementations - JavaScript (used in Mozilla based clients), JScript (used in Internet Explorer and Windows Script Host), ActionScript (used in Adobe Flash), etc.
Some of these implementations - mainly those used in contemporary browsers - are based on 3rd edition of ECMA-262 standard, while others - such as latest ActionScript - on 4th edition of the very same standard. Note that 4th edition is currently abandoned in favor of 5th one, which many browsers have already started implementing.
The test suite for 3rd edition was recently released by Google. The one for 5th edition is currently in the works as well.