But, the definition has a further meaning under a state's penal law. It's why out here we tend to avoid using the term "assault" to describe a fight, since a fight with blows landing tends to be "battery" here. Under state law, an "assault" is an attempted battery. Using the improper definition under state law can get a case tossed. Yes, it is semantics, but THESE semantics have specific meaning under the law. The wrong term changes the meaning and the end result.
In essence, you are BOTH correct ... and, depending upon the context and usage, the term "crime" has different meanings.