Domestic assault offenses come in every level of criminal offense: misdemeanor, gross misdemeanor, and felony. The facts of the case will determine the offense level. The sentence may also increase if there is repeated domestic assault. See https://www.revisor.mn.gov/statutes/?id=609.2242 and https://www.revisor.mn.gov/statutes/?id=609.2243.
Federal domestic violence means that you cross state lines or otherwise implement federal laws in order to kill, injure, harass, or intimidate a spouse or other domestic or dating partner. It also means that you forced or otherwise caused the alleged victim to cross state lines or otherwise implement the federal laws to essentially get away from you to avoid violence. This offense is governed by 18 U.S.C. § 2261. Depending on the effect on the alleged victim (physical harm or death, for example), the sentence could be between five years and life in prison and/or a fine. See https://www.law.cornell.edu/uscode/text/18/2261.
The preceding was a summary of the law. It does not describe all of the elements of the crimes. Laws are also constantly changing. You need to contact a skilled Domestic Assault Attorney Minneapolis to discuss the offenses in detail and with respect to your own particular case. Nothing in this description or anywhere on this site is legal advice.