Assault is defined as the threat of bodily harm that reasonably causes fear of harm in the victim while Battery is the actual physical impact on another person.
If the victim has not actually been touched, but only threatened (or someone attempted to touch them), then the crime is assault.
If the victim has been touched in a painful, harmful, violent, or offensive way by the person committing the crime, this might be battery.
Even a minor touching can qualify as batter providing it is painful, harmful, or offensive to the victim.
Traditionally, if the victim has been actually touched by the person committing the crime, then a battery has occurred. If the victim has not been touched, but only threatened, then the crime is assault. In many states, the distinction between assault and battery has been abolished and either type of action may be charged as an assault.