Assault can be verbal in the U.S., as well. The ADA covered that very point in the class where I renewed my CHL this past weekend.
Here's the subsection from the Texas Penal Code:
§ 22.01. ASSAULT. (a) A person commits an offense if
(1) intentionally, knowingly, or recklessly causes bodily injury to another, including the person's spouse;
(2) intentionally or knowingly threatens another with imminent bodily injury, including the person's spouse; or
(3) intentionally or knowingly causes physical contact with another when the person knows or should reasonably believe that the other will regard the contact as offensive or provocative.
For example, if a husband says to his wife, "If you talk back to me again, I'm going to beat you to a pulp!", he's committed assault.