>ECMAScript is the name of the standard. Each browser implements a (different) subset of it
Supersets, not subsets. In terms of syntax, there is essentially no difference between ECMAScript, JavaScript, and JScript. They're just different implementations of the same thing. In fact, the only reason JScript has a different name is because Microsoft didn't want to license the Java trademark from Sun.
ActionScript is a different animal; it's a superset of ECMAScript and has a lot of additional syntax features, like data type support.
In any case, to work across different browsers, JS code is usually written in the intersection of the ECMAScript superset languages implemented by those browsers. That intersection is ECMAScript.