ECMA script is set of standard rules (set by ECMA international) while JavaScript is implantation of them. So, the JavaScript engine adhere to ECMA standard rules.

ECMAScript is a language specification created by ECMA International, which defines the rules, syntax, and features of a scripting language whereas JavaScript is a programming language that implements the ECMAScript specification. In short, ECMAScript defines the core features and behavior of the language while JavaScript is an implementation of that specification.