The words assault and battery are often used interchangeably in many places, they are two different things.
Battery: The crime requires physical contact that is offensive in some way.
Assault: It is a crime which refers to threat of battery, or attempted battery, without actual physical contact. In some place they don't use the word "battery" an assault means actual physical contact that may be offensive or may cause injury.
Eg: If you tell someone that you are going to shoot him you are committing an offense or assault. If you actually shoot that person without killing him its a battery.