Here is what I have found in Colorado:
"Third degree assault is a Class 1 misdemeanor, and the only assault charge that is not a felony. Third degree assault does not require intent, but rather that a person knowingly or recklessly causes bodily injury to another person or, with criminal negligence, causes bodily injury to another person by means of a deadly weapon. Third degree assault is an extraordinary risk crime that is subject to the modified sentencing range.
Third degree assault is commonly charged in situations involving minor physical altercations that do not involve apparent injury but do involve some degree of physical pain. Third degree assault is often charged in situations alleged to involve domestic violence, for example when a wife says that her husband hit or pushed her, or vice versa, and it hurt.
Harassment misdemeanor is a petty offense and can be committed in a variety of ways, including striking or otherwise making physical contact with another in the absence of pain, use of obscene language or gestures in a public place, following a person, making an obscene phone call, initiating repeated communications, or using fighting language. In order to amount to harassment, these acts must be committed with the intent to harass, annoy, or alarm the alleged victim.
As with third degree assault, harassment is typically associated with incidents alleged to involve domestic violence, such as when a spouse or significant other is accused of pushing the other. "
Both offenses seem to have overlap in their definitions but the sentencing is most likely different. Also, most times people are charged with the most serious offense in the category and then the lesser offenses as well should the facts not sustain the former. This covers the police and District Attorneys.