The terms assault and battery are often used interchangeably on television shows and by individuals to describe those who either threaten to or actually inflict physical harm on another person. To law enforcement and prosecutors in some states, though, they're two distinct criminal offenses.
Put quite simply, an individual may be charged with assault if they threaten or attempt to injure someone else. If they actually make contact with them in either an offensive or harmful way, then they may be charged with battery.
For someone to be found guilty on an assault charge, there has to be a general intent. An individual who acts in a way that's dangerous to others may be charged with assault. This can happen even if there wasn't any proof they intended to inflict harm on a certain individual. Someone who attempts to scare another may, therefore, be charged with assault. Words alone do not warrant such charges though.
It's not necessary for a defendant to have intended to harm their victim to be charged with battery. They need only to have intended to or have actually had contact with them in either a negligent or criminally reckless manner to be charged with this crime.
Accidentally running into someone wouldn't be considered battery. Intentional, offensive or harmful touching that is done without the consent of the victim would be considered to be battery though. Courts rely on the "ordinary person" standard to determine whether an individual's actions were offensive.
Assault and battery are prosecuted independently of each another in some jurisdictions. They're grouped together as a single charge in others. A criminal defense attorney can help you understand how these crimes are prosecuted here in Minnesota and help you craft a defense in your case here in Minneapolis.