In an act of physical violence by one person against another, "assault" is usually paired with battery. In an act of physical violence, assault refers to the act which causes the victim to apprehend imminent physical harm, while battery refers to the actual act causing the physical harm.
Criminal law statutes will sometimes merge the two terms of "assault" and "battery" into the one crime of "assault."
In tort law, the act of assault and battery would be considered an intentional tort.
For more on assault & battery, see this Loyola Law School Law Review article, this ABA article, and this William & Mary Journal of Women and the Law article.