Assault is often defined to include not only violence, but any physical contact with another person without their consent. American common law has traditionally defined assault as an attempt to commit a battery.
In many common law jurisdictions, the crime of battery involves an injury or other contact upon the person of another in a manner likely to cause bodily harm.
the distinction between battery and assault:
the overt behavior of an assault might be A advancing upon B by chasing after him and swinging a fist at his head, while
that of an act of battery might be A actually striking B.