An ECMA-compliant implementation is one that does so according to the precepts laid down in the ECMA 262 standard. This would be an ECMAScript interpreter although it should also state what edition of the standard it is compliant with.
A DOM-compliant interpreter would be compatible with DOM level 1 or level 2. Other levels are in the course of being standardized.
An implementation will usually supply additional functionality over and above that specified by the standard.