There’s no ambiguity. Emoji are characters in the emoticons code block (U+1F600…U+1F64F). Emoji are indeed a subset of characters, but anything outside that block is not an emoji.
Edit: jumped the gun on that definition, just took the code block from Wikipedia. But there is no ambiguity on which character is an emoji and which is not. The Unicode Consortium publishes lists of emoji and guidelines on how they should be rendered.