When you’re talking about an actual criminal charge, state law defines the crime. Dictionary definitions are irrelevant. The linked story is about Georgia. So…
Simple Assault:
Attempting to commit a violent injury on someone else or putting them in a situation where it’s reasonable they can be injured in such a manner. No actual physical touching is necessary to violate the law. Words can be enough. For example, threatening to break someone’s neck, if done in a menacing manner, can be considered simple assault.
Aggravated Assault: Assaulting someone:
(1) With intent to murder, to rape, or to rob;
(2) With a deadly weapon or with any object, device, or instrument which, when used offensively against a person, is likely to or actually does result in serious bodily injury; or
(3) Shooting a firearm from within a motor vehicle toward a person or persons.
Simple Battery:
(1) Intentionally making physical contact of an insulting or provoking nature with the person of another; or
(2) Intentionally causing physical harm to another person.
Aggravated Battery:
Intentionally and maliciously inflicting a serious injury to the victim, such as loss of a limb, loss of use of a limb, or serious disfigurement.
Copied from Findlaw – Georgia Assault and Battery Laws