Not a lawyer, but I have a wife who is a school district administrator and deals with the local PD regarding assault and battery more than she should. Assault does not necessarily mean actually touching the person. The threat of an action towards an individual which conveys the threat of physical harm can result in an assault charge. Conversely an assault charge can also be levied for minor unwanted physical contact that does not result in bodily harm. For example a coach putting his hand on the back of a player and pushing them towards the dugout can result in an assault charge even if there was no physical harm.
Generally adding battery to the charge, ie "assault and battery" vs "assault" means that physical harm was done. Using the same example the coach grabbing a player by the neck, squeezing and dragging the player into the dugout would most likely result in some physical pain and then an assault and battery charge will be levied instead of an assault charge.